Question

A football is to be thrown by a quarterback to a receiver who is running at a constant velocity of 11.2 m/s directly away from the quarterback, who intends for the ball to be caught a distance of 34.0 m away. At what distance should the receiver be from the quarterback when the ball is released? Assume the football is thrown at an initial angle of 45.0° and that it is caught at the same height at which it is released.

Answer 1

Range = v_o²sin2θ / g = 34

=> v_o = [34 * 9.81 / sin90^o]^1/2 = 18.263 m/s

Time taken for ball to reach the receiver,

t = 2v_o(sin45^o)/g = 2 * 18.263 * sin45^o / 9.81 = 2.633 s

Distance travelled by receiver, d = 11.2 * 2.633 = 29.5 m

So, initial position of receiver = 34 - 29.5 = 4.5 m