Projectile a is fired with velocity v at an angle of 30 The speed of the projectile at an altitude h is A projectile is fired with an initial speed of 46. which of the following pairs of graphs best represents the vertical components of the velocity and acceleration, v and a, respectively, of the projectile as functions of time t? A Projectile is fired at an angle of 60 ∘ to the horizontal with an initial velocity of 800 m / s : Find the time of flight of the projectile before it hits the ground . A projectile is launched at an angle to the horizontal and rises upwards to a peak while moving horizontally. [g = 10 m/s\ (^2\)] A projectile is fired up the inclined plane with the initial velocity shown. 0 s after launch compare with its horizontal component of velocity 2. Since cos (30°) > cos (40°), the horizontal component of velocity for projectile A is larger than that of projectile B. Calculate the velocity attained after 1s. Enter velocity, angle & gravity to get instant results with formula and steps. Use g =9. Ignoring the effects of air resistance, at what angle must the golfer A cannonball is fired with initial speed v o at an angle 30 degrees above the horizontal from a height of 40 m above the ground. What is the horizontal component of its velocity after 4. Example 4. Projectile A is fired with velocity v at an angle of 30. Its time of fight is `T`. (a) If a gun is fired with A=30∘ and V=500 Learning Objectives By the end of this section, you will be able to: Identify and explain the properties of a projectile, such as acceleration due to gravity, range, maximum height, and trajectory. The approximate velocity of the projectile at time T 4 is ≈145m/s. --- A projectile is fired with a velocity 'u' making an angle θ with the horizontal. ) The following If a projectile (such as a bullet) is fired into the air with an initial velocity v at an angle of elevation θ (see Figure 9 ), then the height h of the projectile at time t is given by h = − 16 t 2 + v t sin θ Find the angle of elevation of a rifle, if a bullet fired at 1,500 feet per second takes 3 seconds to reach a height of 750 feet. Find the maximum height of the cannonball. Jul 22, 2014 · Projectile Motion Example Problem: A cannon is fired with muzzle velocity of 150 m/s at an angle of elevation = 45°. It happens when an object has an initial forward velocity and is pulled downward by gravity, causing it to follow a predictable arc-shaped path. A projectile launched on level ground with an initial speed v0 at an angle θ above the horizontal… will have the same range as a projectile launched with an initial speed v0 at 90° − θ. Apr 5, 2024 · To find the magnitude of the vertical component of the velocity at the time the projectile is fired, we can use trigonometric functions. A cannonball is fired with initial speed v o at an angle 30 degrees above the horizontal from a height of 40 m above the ground. (a) Show that, at time t, the horizontal displacement is x = 45 (1 - -1/3). A second projectile is then fired with the same initial speed 0. 8 m / s 2). 8 m/s2). What maximum height will it reach and how far will it fly horizontally? Projectile A is fired with a velocity of 20 m/s at an angle of 30° below horizontal as shown in Figure P10–45 and lands 2. 81 m⋅s−2 Provide the following values: t0,x =…s x0 =[m t0,y = [m y0 =[m= y0+y -distance to target yf =… (You must provide an answer before moving to the next part. ) From the top of a hill inclined at an angle of 30° a projectile is fired with a velocity of 50 ft. At what velocity must a second projectile B be fired at an angle of 50° above horizontal if it is to land at the same location as A? v x = v 0x, x = x 0 + v 0x t, v y = v 0y + a y t, y = y 0 + v 0y t + ½a y t 2. Mar 12, 2020 · If a projectile is fired with an initial velocity of V meters per second at an angle A above the horizontal and air resistance is assumed to be negligible, then its position after t seconds is given by the parametric equations x= (Vcos (A))t, y= (Vsin (A))t−12gt2, A gun is fired with a = 30° and v0 = 500 m/s. The projectile is fired at an angle of 30° with an initial speed of 40 m/s. Jan 2, 2024 · A projectile is fired from a cannon at a 30∘ angle with the ground and an initial velocity of 100m/s. Show that its trajectory is a parabola. 0 degrees above the 1 point horizontal. Identify and explain the properties of a projectile, such as acceleration due to gravity, range, maximum height, and trajectory. Jan 1, 2012 · The final vertical velocity is calculated after 3 seconds, and the final speed is determined by combining the horizontal and vertical components using vector addition. We need to calculate the radius of curvature of the path at the instant when the magnitude of rate of change of speed of projectile is minimum. Compute the maximum height h, measured perpendicular to the plane, that is reached by the projectile. The acceleration of free fall is g. It lands at point Q, a horizontal distance R from P, after time T. How far along the slope and with what velocity will the projectile strike the ground? A projectile is fired with an initial velocity of 60 m/sec. Find the angle θ of the second projectile so that they will collide. What is the magnitude and direction of its velocity 5 seconds after launch? If a projectile is fired with an initial velocity of v0 meters per second at an angle a above the horizontal and air resistance is assumed to be negligible, then its position after t seconds is given by the parametric equations x = (v 0 c o s a) t, y = (v 0 s i n a) t 1 / 2 g t 2 x = (v0cosa)t,y = (v0sina)t −1/2gt2 where g is the acceleration due to gravity (9. 0m/s2. ° above the horizontal. When will the bullet hit the ground? A projectile is fired with 10ms^-1 at an angle of 60o with horizontal. Now we have to find the speed of the projectile when its direction of motion. Projectile B is fired with velocity v at an angle of 40. At what distance x from the gun will be projectile strike the ground? Projectile A is fired with velocity v at an angle of 30 degrees above the horizontal. A projectile is fired with a speed of v = 60 m/s at an angle of 60°. ) Example: Motion of a Cannonball During an Independence Day celebration, a cannonball is fired from a cannon on a cliff toward the water. If the ground is level, what is the maximum height reached by the projectile? Oct 16, 2023 · When solving the projectile motion problem for a projectile fired with an initial velocity of v0 = 45m/s at an angle of 53° above the horizontal, we can break down the problem into several parts: the time in the air, horizontal range, maximum height, and velocity at the highest point. Air resistance is proportional to the velocity. 1 - Projectile Motion Calculator and Solver Given Initial Velocity, Angle and Height Enter the initial velocity V0 in meters per second (m/s), the A projectile is fired a velocity of 150 meters per second at an angle of 30° with the horizontal. 0 points A projectile is fired with an initial speed vo at t 0. (see the figure. A projectile is fired from the edge of a 150-m cliff with an initial velocity of 180 m/s at an angle of 30 degree with the horizontal. Notice that the acceleration from gravity term (1/2gt²) only applies to the vertical motion. Apr 30, 2025 · Struggling with projectile motion? Learn quickly how to break it into components, solve real problems, and avoid exam mistakes to ace your exam! A projectile is fired at an angle of 30° to the horizontal with a velocity of 40 m/s Calculate the velocity attained after 1 s. What maximum height will it reach and how far will it fly horizontally? Solution The first step in the analysis of this motion is to resolve the initial velocity into its vertical and horizontal components. 2 v 0. During its motion,its velocity,when it makes 30o to horizontal is View Solution Nov 20, 2023 · The range R of a projectile fired with an initial velocity of 150 m/s and at an angle of 45 degrees is approximately 2300 m, assuming it lands at the same height it was launched from. Find the relevant formula with examples for better understanding. Sep 11, 2023 · To find the velocity attained by the projectile after 1 second, we first need to break down the initial velocity into its horizontal and vertical components. . A golfer strikes a golf ball at 120 feet per second. shows different paths for the same object launched at the same initial velocity at different launch angles. The firing velocity is 450 m/s. The target is some distance away, and its elevation is h below the initial firing. Question: If a projectile is fired with an initial velocity of V meters per second at an angle A above the horizontal and air resistance is assumed to be negligible, then its position after t seconds is given by the parametric equations x= (Vcos (A))t,y= (Vsin (A))t−21gt2, where g is the acceleration due to gravity (9. The question involves calculating the vertical component of a projectile's velocity when fired at an angle to the horizontal. A projectile is fired at an angle of 30° to the horizontal up a slope that is at 10° to the hori- zontal. Initial speed is V and this a… Jan 30, 2020 · If a projectile is fired with an initial velocity of V meters per second at an angle A above the horizontal and air resistance is assumed to be negligible, then its position after t seconds is given by the parametric equations x= (Vcos (A))t, y= (Vsin (A))t−12gt2, A gun is fired with a = 30° and v0 = 500 m/s. The horizontal distance traveled by a projectile is called its range. 8 m/s^2). If a projectile is fired from the origin with an initial velocity of v 0 meters per second at an angle α above the horizontal and air resistance is assumed to be negligible, then its position after t seconds is given by the parametric equations x = (v 0 cos α) t y = (v 0 sin α) t − 1 2 g t 2 where g is the acceleration due to gravity (9. Aug 19, 2025 · Solution For A projectile is fired at an angle of 30° to the horizontal with an initial velocity of 45 m/s. The projectile strikes the ground with a speed of 1. 0 m/s at an angle of 45° above the horizontal. Additionally, determine the position (x, y) where the collision will occur. where v is the initial velocity, Θ is the angle of projectile, and (x₀,y₀) are the initial starting coordinates (usually 0). 7 m/s v i Accurately calculate projectile range with our free online calculator. Projectile motion is a form of motion in which an object or particle (called a projectile) is thrown with some initial velocity near the earth’s surface, and it moves along a curved path under the action of A projectile is to be launched at an angle of 30° so that it falls beyond the pond of length 20 meters as shown in the figure. (a) If a gun is fired with α = 30 A projectile is fired from point P with velocity V at an angle θ to the horizontal. 5 s later. Jun 10, 2025 · Projectile motion is the motion of an object that is thrown or launched into the air and moves along a curved path due to the force of gravity. If a projectile is fired with an initial velocity v at an angle of inclination θ from the horizontal, then its trajectory, neglecting air resistance, is the parabola Jul 10, 2023 · To solve the problem of projectile motion for a projectile fired at an initial velocity of 50 m/s at an angle of 30 degrees above the horizontal, we can break the motion into horizontal and vertical components. a projectile is fired with the initial velocity Vo at angle theta with the horizontal and follows the trajectory shown above. This calculation uses the range formula for projectile motion and applies specific values for initial velocity and gravity. A projectile is fired with an initial speed of 46. A projectile fired from a gun has initial horizontal and vertical components of velocity equal to 30 m/s and 40 m/s, respectively. Note that both cannonballs have the same vertical position over time. What value of α maximizes the range (the horizontal distance traveled)? Dec 20, 2021 · The initial velocity of the projectile is given as 320 m/s, and it is fired at an angle of 30 degrees from the horizontal. (b) Calculate the horizontal range. Apply the principle of independence of motion to solve projectile motion problems. Sep 10, 2023 · A projectile is fired with an initial velocity of 30m/s at an angle of 60∘ above the horizontal. Nov 10, 2023 · To find the maximum height of a projectile, we need to analyze its motion. A second projectile is then fired with the same speed 0. Use one-dimensional motion in perpendicular directions to analyze projectile motion. Determine the location and velocity of a projectile at different points in its trajectory. Give your answer to the nearest tenth of a degree. a) What is the maximum height the projectile reaches? b) What is the total time aloft? c) How far away did the projectile land? (Range) d) Where is the projectile at 10 seconds after firing? Let’s set up Nov 14, 2021 · VIDEO ANSWER: In this problem we have given projectile A is fired with velocity V at an angle of 30 degree. 66 m/s of a projectile fired at 30° with an initial speed of 10 m/s, for the horizontal component of the initial velocity. The maximum height can be calculated using the equations for horizontal and vertical components of velocity, as well as the equations for time and displacement in projectile motion. v i−up = (100. Analysis of projectile motion involves dealing with two motions independently. Dec 27, 2024 · Solution For A projectile is fired with initial velocity of v= 300m/s at an angle 30° with horizontal. (b) Find a similar expression for the A projectile is fired a velocity of 150 meters per second at an angle of 30° with the horizontal. If air resistance is 2 answers A projectile fired from the edge of a 150 m high cliff with an initial velocity of 180 m/s at an angle of elevation of 30 deg 3 answers The muzzle velocity of a projectile fired from a gun has an upward component of 49 m/s and a horizontal component of 60 m/s A projectile is fired from a cliff 300 m high with an initial velocity of 400 m/s. Thus the equations of motion are dt2 and dt = -9 where it is known that k = }. Feb 14, 2023 · A projectile is fired from the origin with a velocity v0 at an angle θ with the x -axis. Find v 0. which of the following pairs of graphs best represents the vertical components of the velocity and acceleration, v and a, respectively, of the projectile as functions of time t? Projectile Motion Calculator and Solver An online calculator to calculate the maximum height, range, time of flight, initial angle and the path of a projectile. 6 m/s at an angle of 42. Calculate the trajectory of a projectile. To solve the problem step by step, we will follow the concepts of projectile motion. 707)=70. The velocity of the projectile when it hits the slope is ____________ the initial velocity vo. At an angle of data with the horizontal. Upon reaching the peak, the projectile falls with a motion that is symmetrical to its path upwards to the peak. The angle between the initial velocity vo and the horizontal plane is a. Assuming no air resistance and g = 10m/s2, calculate the time it will spend in the air. Air resistance is negligible. The vertical component of the initial velocity (v_y) can be found using the sine function: Nov 1, 2025 · A cannon ball is fired with an initial velocity of 100. (c) Find the initial velocity required to fire a projectile 300 feet at an angle of θ = 40 ∘ (d) For a given initial velocity, what angle of elevation yields a maximum range? Explain. To calculate projectile motion at an angle, first resolve the initial velocity into its horizontal and vertical components. Sep 1, 2023 · If a projectile is fired with an initial velocity of V meters per second at an angle A above the horizontal and air resistance is assumed to be negligible, then its position after t seconds is given by the parametric equations x= (Vcos (A))t, y= (Vsin (A))t−12gt2, A gun is fired with a = 30° and v0 = 500 m/s. This is projectile A. The position vector r and the velocity vector v at time t have only components along the x- and y-axes. A projectile is fired with an angle of elevation α and initial velocity v 0 . meters per second at an angle of 30o with the horizontal. Note that no acceleration is acting in this direction, as gravity only acts vertically. How far along the slope and with what velocity will the projectile strike the ground? Use one-dimensional motion in perpendicular directions to analyze projectile motion. 0 seconds? With this horizontal projectile motion calculator, you'll quickly find out the trajectory, time of flight, and projectile range. To determine the projectile range it is necessary to find the initial velocity, angle, and height. We usually specify the horizontal range in meters (m). Use g=9. 8 m/s 2. Determine the angle θ of the second projectile so that the two projectiles collide. May 25, 2022 · (b) Find the range r if the initial velocity of a projectile is 80 feet per second at an angle of θ = 42 ∘. A projectile is fired at an angle of 30∘ to the horizontal up a slope that is at 10∘ to the horizontal. Aug 9, 2025 · A projectile is fired with a speed of v = 60 m/s at an angle of 60° . 1 - Projectile Motion Calculator and Solver Given Initial Velocity, Angle and Height Enter the initial velocity V0 in meters per second (m/s), the A projectile is fired with velocity V = 30 m/s at an angle of 45° to the horizontal. If v is the initial velocity, g A projectile is launched from point O at an angle of 22° with an initial velocity of 15 m/s up an incline plane that makes an angle of 10° with the horizontal. Projectile motion is the motion of an object thrown (projected) into the air when, after the initial force that launches the object, air resistance is n Question: If a projectile is fired with an initial velocity of v0 meters per second at an angle α above the horizontal and air resistance is assumed to be negligible, then its position after t seconds is given by the parametric equations x = (v0 cos α)t y = (v0 sin α)t −1/2gt^2 A projectile is fired at speed v on a flat surface at an angle 30 above the horizontal. Using the equations mentioned above, we can determine the baseball’s range, time of flight, and maximum height. (Identical projectiles launched at complementary angles have the same range. A projectile is fired with initial velocity of v= 300m/s at an angle 30° with horizontal. Examples include a ball being thrown, a rocket launched at an angle, or water sprayed from a hose. Calculate the range, time of flight, and maximum height of a projectile that is launched and impacts a flat, horizontal surface. If a second projectile is launched with the same initial velocity but at an angle of 60 degrees above the horizontal. The horizontal displacement of the projectile is called the range of the projectile. Predictable unknowns include the time of flight, the horizontal range, and the height of the projectile when it is at its peak. The projectile equations and parameters used in this calculator are decribed below. A projectile launched at an initial velocity of v0 at an angle 30 degrees above the horizontal. 0 s after launch, ignoring air resistance? Aug 1, 2017 · The range of a projectile fired at an angle θ with the horizontal and with an initial velocity of v0 feet per second is given by the formula: r = gv02 sin(2θ) where r is measured in feet and g is the acceleration due to gravity (approximately 32 feet per second squared). Gravity = 9. 2° above the horizontal on a long flat firing range. A projectile is fired at an angle of 30° to the horizontal with a velocity of 40 m/s Calculate the velocity attained after 1 s. How does the horizontal component of its velocity 1. /sec. A projectile is fired with an initial speed of 30 m/s at an angle of 60 degrees above the horizontal. A projectile is fired at an angle of `30^ (@)` to the horizontal such that the vertical component of its initial velocity is `80m//s`. Q: Why does the angle affect the range? A: The angle determines the balance between horizontal and vertical velocity components. How long will it take for the cannonball to 5. Complete answer: As per the problem we know that a projectile is fired with velocity v at an angle θ with horizontal. Question Projectile A is fired with velocity v at an angle of 30. 31 seconds later. The object’s maximum height is the highest vertical position along its trajectory. Which equation is correct? Projectile 1 is fired from ground level with velocity v1 at an angle θ1, while projectile 2 is fired at velocity v2 from a height h above the ground, as shown in the diagram below. Projectile B is fired with velocity v at an angle of 40 degrees above the horizontal. At what distance x from the gun will be projectile strike the ground? Jul 23, 2019 · In this article find Projectile motion formula for an object fired at an angle and for the object fired horizontally. Sep 7, 2023 · A projectile is launched at an upward angle of 30 degrees to the horizontal with a speed of 30 m/s. Frequently Asked Questions (FAQ) Q: What does projectile motion mean? A: It refers to the motion of an object launched into the air, subject only to gravity and its initial velocity, following a parabolic trajectory. Find the distance R to the point of impact. (A) How much higher or lower is the launch point relative to the point where the projectile hits the ground? (B) To what maximum height above the launch point does the projectile rise? A projectile is fired at an angle of 30° to the horizontal with a velocity of 40ms^ (-1). View Solution Projectile Motion Calculator and Solver An online calculator to calculate the maximum height, range, time of flight, initial angle and the path of a projectile. (a) Calculate the time of flight. At what position (x, y) will this happen? Nov 1, 2010 · A projectile is fired with a velocity of 150. 1 A cannon ball is fired with an initial velocity of 100. A projectile is fired with the initial velocity v0 at an angle θ. Projectile Problems Technique in SolvingProblem:A projectile is fired from the edge of a 150-m cliff with an initial velocity of 180 m/s at an angle of 30° w A projectile is given an initial velocity vo at an angle f above the horizontal. (Ignore any effects due to air resistance. 0 meters per second at an angle θ above the horizontal. 2° above the horizontal on Introduction to Projectile Motion - Formulas and Equations A projectile is launched at an angle to the horizontal and rises upwards to a peak while moving horizontally. Determine (a) the maximum height reached by the projectile, (b) the Dec 5, 2019 · A projectile is fired with an initial velocity of 120. Figure 5. The cliff is 100 f t above the water (Figure 7). Understanding these concepts is crucial for solving projectile motion problems effectively. The cannon is aimed at an angle of 30 ∘ above horizontal and the initial speed of the cannonball is 600 f t / s e c. Enhanced with AI, our expert help has broken down your problem into an easy-to-learn solution you can count on. above a level plain. Which of the following pairs of velocity-time graphs represents the horizontal and vertical components of velocity, V, and wy, of the projectile, as functions of time? V V V2 V2 -V2 -V2 V V2 o -V2 -V2 V V V2 V2 O -V2 -V2 V 12 -V/2 -V/2 -V The projectile range is the distance the object will travel from when you fire it until it returns to the same height at which it was fired. 81 m⋅s−2 Recall yf (t)= −7 m What is the horizontal distance (in m ) traveled to reach the target? Q: A projectile is fired with a velocity v = 10m/s at right angles to the slope, which is the inclined at an angle 0 = 30° with the horizontal. What is the magnitude of the vertical component of the velocity at the time the projectile is fired? Maximum Height of Projectile After understanding what a projectile is, let us know the maximum height of the projectile. If the firing angle is 30 degrees from the horizontal, compute the horizontal range of the projectile. What is the magnitude of the vertical component of the velocity at the time the projectile is fired? Identify and explain the properties of a projectile, such as acceleration due to gravity, range, maximum height, and trajectory. Find the time of flight and impact velocity of a projectile that lands at a different height from that of launch. What is the magnitude of the vertical component of the velocity at the time the projectile is fired? Sep 19, 2022 · 58. 7 m/s v i A projectile A is fired with velocity v at an angle of 30 degrees above the horizontal. The object hits the ground 7. 0 m/s) (0. upward at an angle of 30° to the horizontal from a point 80 m. 3. Take g = 10 m/s. The range of the projectile depends on the object’s initial velocity. ) Assuming that air resistance is negligible and the only external force is due to gravity, find the position function r (t) of the projectile. 85. Let’s calculate the projectile motion of a baseball thrown with an initial velocity of 30 m/s at a launch angle of 45 degrees. Jul 7, 2021 · If a projectile is fired with an initial velocity of V meters per second at an angle A above the horizontal and air resistance is assumed to be negligible, then its position after t seconds is given by the parametric equations x= (Vcos (A))t, y= (Vsin (A))t−12gt2, A gun is fired with a = 30° and v0 = 500 m/s. The range is a crucial component of projectile motion because it describes how far the object will travel given a specific initial velocity and launch angle. Determine the initial speed of the projectile. Nov 5, 2020 · The angle at which the object is launched dictates the range, height, and time of flight it will experience while in projectile motion. The range of a projectile is dependent on several factors: the initial speed at which the object is launched, the angle of launch, and the acceleration due to gravity. (c) Calculate the maximum height reached. If a gun is fired A cannonball is fired with initial speed v 0 at an angle 30 degree above the horizontal from a height of 40 m above the ground. The initial velocity is given as 150 meters per second at an angle of 30 degrees with the horizontal. 0 m/s) (sin45∘)= (100. In this case, the projectile is fired with a velocity of 320 m/s at an angle of 30 degrees with the horizontal. 28 The diagram shows the projectile motion of a cannonball shot at a horizontal angle versus one dropped with no horizontal velocity. ) will have a maximum range when θ = 45°. Initial speed is V and this a… Oct 5, 2025 · A projectile is fired with a velocity of 20 m/s at an angle of 30° to the horizon. How far along the slope and with what velocity will the projectile strike the ground? 10. Determine: (i) Time of ascent (ii) Time of flight (iii) Maximum height reached. a) What is the range of values of the initial velocity so that the projectile falls between points M and N? Consider a projectile being launched at an initial velocity v 0 in a direction making an angle θ with the horizontal. Let vO = 150 m⋅s−1,θ=30 degrees, and h=7 m. What horizontal distance will it cover before it strikes the plain? Mar 13, 2023 · A projectile is fired from ground level with a speed of 150 m/s at an angle of 30° above the horizontal on an airless planet where g = 10. Mar 21, 2024 · The vertical component of a projectile's velocity fired at a 30° angle with an initial speed of 150 m/s is 75 m/s, calculated using the sine function. We assume that air resistance is negligible and the only force acting on the object is the force of gravity with acceleration g = 9. Neglecting air resistance, find (a) the horizontal distance from the gun to the point where the projectile strikes the ground, (b) the greatest elevation above the ground reached is the projectile. 5 seconds later. A projectile is fired with an initial speed of 1000 m/s at an angle of 37 degrees above the horizontal. A projectile is fired from the surface of the Earth with a speed of 200 meters per second at an angle of 30° above the horizontal. If the projectile is positioned perpendicular to the surface of the hill, determine its range down the hill. A projectile is launched from point O at an angle of 22° with an initial velocity of 15 m/s up an incline plane that makes an angle of 10° with the horizontal. VIDEO ANSWER: In this problem we have given projectile A is fired with velocity V at an angle of 30 degree. Determine the relationship between the magnitudes of the horizontal components of velocity for projectiles A and B. Let v0 = 150 m⋅s−1,θ=30 degrees, and h=7 m. If the projectile's initial horizontal speed is 55 meters per second, then angle θ measures approximately how much? 017 (part 1 of 3) 10. Jan 17, 2022 · VIDEO ANSWER: In this question, we have given that a project that is fired with the velocity V. May 4, 2024 · The speed at the maximum height is 8. By choosing a convenient orientation of our coordinate system we have simplified the mathematics involved in solving a projectile motion problem. If the ground is level, what is the maximum height reached by the projectile? A projectile is fired with an angle of elevation α and initial velocity v 0 . qkvtp hrj queeo yseayj olkt zptouw plwtioi dmzwxw bgqn nvtferb lwygf hssz cmvm nlbh qzxbvbo