New england patriots quarterback tom brady throws a football straight toward a receiver with an initial speed of 16.0 m/s, at an angle of 25.0° above the horizontal. at that instant, the receiver is 16.5 m from the quarterback. with what constant speed should the receiver run?

Hello
This question requires us to deal with the football as a projectile. Therefore, we will assume that the ball is caught at the same height from which it was thrown.
To see how far the ball will travel, we use the formula for the range of a projectile that is:
Range = [(initial velocity)^2 * sin(2*angle to horizontal)]/g
Given that the initial velocity is 16 m/s, the angle to the horizontal is 25 and g is 9.81 m/s^2, R works out to be:
almost 20.0 m
The distance the receiver will have to run will be:
20 - 16.5 = 3.5 m
The time of the ball's flight will be equal to the time the receiver has to get to the ball. The ball's flight time is given by:
time = [2 * (initial velocity) * sin(angle from horizontal)] / g
time = 1.38 seconds
Therefore, the receiver's speed must be:
3.5 / 1.38 = 2.54 m/s