Question

Kids are playing ball for recess. The ball is kicked from the ground with an initial velocity of 50ft/sec. Use the projectile motion equation to determine how long the catcher has to get into position it be catches the ball 6 feet in the air on its way down.

Answer 1

0.12 s

Explanation:

initial velocity of projection, u = 50 ft/s

range, R = 6 feet

Let θ is the angle of projection.

Use the formula for the horizontal range.

`R = (u^(2)Sin2\theta)/(g)`

`6 = (50^(2)Sin2\theta)/(32)`

Sin 2θ = 0.0768

2θ = 4.4 degree

θ = 2.2 degree

The formula for the time of flight is

T = 2 u Sin θ/g

T = 2 x 50 x Sin 2.2 / 32

T = 0.12 second

thus, the time required is 0.12 s.