![]() Assuming that v 2 /g is constant, the greatest distance will be when sin(2) is at its maximum, which is when 2 90 degrees. ![]() That's it! We've derived the trajectory formula. The equation for the distance traveled by a projectile being affected by gravity is sin(2)v 2 /g, where is the angle, v is the initial velocity and g is acceleration due to gravity. Vertical motion under the influence of gravity can be described by the basic motion equations. 1 Im trying to find the initial velocity of a tennis ball (magnitude and angle) given the initial height, max height and max range. (That is, we pretend the Earth is flat and non-rotating.) Also, we assume gravity is constant. is the initial Use velocity differentials in feet to. 1 Ill make the usual first-year physics assumptions that there is no air resistance and no effects from the curvature of the Earth or from the Earths rotation. ![]() First, we plug the initial velocity ( v0. These equations are all we need to solve flight time and flight distance for a projectile that is launched from ground level (an initial height of zero). y = h V y t − g t 2 / 2 y = h V_y t - g t^2/2 y = h V y t − g t 2 /2Īs the launch velocity ( V 0 V_\text y = h x tan α − 2 V 0 2 c o s 2 α g x 2 Projectile Motion The range R of a projectile is R v02 (sin 2) 32 where angle of v0 elevation. After rearranging and simplifying the equations to solve for projectile motion, they are given as: vx v0cos () vy v0sin () t 2vy/g.Where does the vertical distance formula come from?įirst, let's remember the equations of motion for the horizontal ( x x x) and vertical ( y y y) positions: ![]()
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