A football is to be thrown by a quarterback to a receiver who is running at a co

Question

A football is to be thrown by a quarterback to a receiver who is running at a constant velocity of 11.4 m/s directly away from the quarterback, who intends for the ball to be caught a distance of 36.6 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.(PLEASE SHOW WORK) Below is some help that our instructor has provided but I am still not getting the correct answer and have also posted this question multiple times on chegg and also recieved no correct answer.

Explanation / Answer

Let the horizontal Velocity of football = vo * cos(45)
Let the Vertical Velocity of football = vo * sin(45)

Horizontal distance = 36.6 m
time t = 36.6/(vo * cos(45))

Vertical Distance = 0

s = vo * sin(45) *t - 1/2 * 9.8 * t^2
4.9 * t = vo * sin(45)
4.9 * 36.6/(vo * cos(45)) =  vo * sin(45)
4.9 * 36.6 = vo^2 * sin(45) * cos(45)
vo = 18.94 m/s

t = 36.6/(18.94 * cos(45))
t = 2.73 s

Now let us say, receiver is x meter away from quarterack when ball is released.
Distance receiver need to travel = 36.6 - x
time, t = 2.73
speed = 11.4 m/s

Distance = speed * time
36.6 - x = 11.4 *  2.73
x = 5.48 m
Distance should the receiver be from the quarterback when the ball is released, x = 5.5 m

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