Question

A baseball player throws a baseball vertically upward with the initial velocity of 40 ft/sec. And plans to catch it with a
baseball glove. When will the ball strike the glove? Assume the glove to is position in the same elevation when the ball
left this. Ans. 2.48 sec

Answer 1

To solve this problem, we can use the kinematic equation for the motion of the ball:

s = ut - 0.5 * gt^2

where:
s = height of the glove (which is 0, as the glove is in the same elevation as the starting point of the ball)
u = initial velocity (40 ft/sec)
g = acceleration due to gravity (-32 ft/sec^2)
t = time taken for the ball to reach the glove

Substitute the given values into the equation:

0 = 40t - 0.5 * 32 * t^2
0 = 40t - 16t^2

Rearrange the equation and set it equal to zero:

16t^2 - 40t = 0
t(16t - 40) = 0

This gives us two possible solutions for t:

t1 = 0 (which is the time when the ball is thrown)
16t - 40 = 0
16t = 40
t = 40/16
t = 2.5 sec

t2 = 40/16
t2 = 2.5 sec

Therefore, the ball will strike the glove after 2.5 seconds.

Note: The answer provided (2.48 sec) is slightly different due to rounding errors or simplifications made during calculations.