Question

How long will it take for a ball thrown up in the air with an initial velocity of v to reach a height equal to its initial value?

Answer 1

To determine the time it takes for a ball thrown up in the air with an initial velocity $v$ to reach a height equal to its initial value, we can use the kinematic equation for vertical motion:

$h=v_{i}t-\frac{1}{2}g{t}^2$

where:

• $h$ is the height of the ball
• $v_i$ is the initial velocity of the ball
• $t$ is the time taken by the ball to reach the desired height
• $g$ is the acceleration due to gravity (approximately $9.8{\text{m/s}}^2$)

In this case, we want the height $h$ to be equal to the initial height, which we'll denote as $h_0$. Thus, the equation becomes:

$h_0=v_{i}t-\frac{1}{2}$