The range (maximum horizontal distance) travelled by a projectile is given by the formula
R = V^2(sin 2A)/g
where
R = range
V = initial velocity of ball = 64 ft/sec. (given)
A = angle of launch = 45 degrees (given)
g = acceleration due to gravity = 32.2 ft/sec^2 (constant)
Substituting values,
R = 64^2(sin 2*45)/9.8
R = 127.20 feet
Since the receiver is 60 yards away (180 feet), he will have to travel a distance of 180 - 127.20 = 52.80 feet to catch the ball.
The ball's total travel time is given by the formula
T = 2V(sin A)/g
where all the terms have been previously defined.
Substituting values,
T = 2(64)(sin 45)/32.2
T = 2.82 sec.
Therefore, in order for the receiver to catch the ball, his speed must be equal to
52.80/2.82 = 18.72 ft/sec.
Hope this helps ya
