Question

A football is to be thrown by a quarterback to a receiver who is running at a constant velocity of 10.4 m/s directly away from the quarterback, who intends for the ball to be caught a distance of 38.4 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

The range of projectile on level of ground which is given as :

using an equation,    R = v_r² sin 2 / g                                                         { eq.1 }

where, v_r = initial velocity of the receiver = 10.4 m/s

g = acceleration due to gravity = 9.8 m/s²

inserting the values in above eq.

R = (10.4 m/s)² sin (2 x 45⁰) / (9.8 m/s²)

R = (108.1 m²/s²) / (9.8 m/s²)

R = 11.03 m

time taken by the receiver which is given by :

x = v_ox t (v₀ cos ) t

t = x / (v₀ cos )                                                                                        { eq.2 }

x = horizontal distance between quarterback & receiver = 38.4 m

inserting the values in eq.2,

t = (38.4 m) / [(10.4 m/s) cos 45⁰]

t = (38.4 m) / (7.35 m/s)

t = 5.22 sec