Question

A baseball is hit from theground straight up into the airwith a speed of 14.6 m/s. Howlong is the ball in air (time inseconds from ground-to-ground)?

Answer 1

Givens.

• Initial speed = 14.6 m/s.

,

• FInal speed = 0 m/s (at highest point).

,

• Gravity = 9.8 m/s^2.

First, find the time needed to reach the highest point.

`\begin{gathered} v_f=v_0+gt \\ t=(v_f-v_0)/(g) \\ t=(0-14.6\cdot(m)/(s))/(-9.8\cdot(m)/(s^2)) \\ t\approx1.49\sec \end{gathered}`

It takes 1.49 seconds to reach the highest point.

The time that the baseball takes to reach the ground is double t because the trajectory is symmetrical, that is, it takes the same time to go from ground level to highest point than from highest point to ground level.

`t_{\text{total}}=2\cdot1.49\sec =2.98\sec`

Therefore, the baseball is 2.98 seconds in the air.