Question

A football is kicked off with an initial speed of 64 ft/s at a projection angle of 45o. A receiver on the goal line 60 yd away in the direction of the kick starts running to meet the ball at that instant. Calculate his average speed if he is to catch the ball just before it hits the ground. Neglect air resistance.

Answer 1

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