Question

crall decides that with the kinematic equations of motion and the value of g (9.81 m/s²) she should be able to make quantitative predictions of the balls motion. she decides to release the ball at a height of 40 m above the ground and that she wants the ball to hit the ground at time 4 s later. she then calculates the speed the elevator needs to be traveling in order for the ball to reach the ground at this time. which is the correct result of cralls calculation? 29.6 m/s 68.4 m/s -9.6 m/s 9.6 m/s

Explanation:

Step1: Identify the kinematic equation

Use the equation $y - y_0=v_0t-\frac{1}{2}gt^2$. Here, $y - y_0=- 40$ m (down - ward direction is negative), $t = 4$ s and $g = 9.81$ m/s².

Step2: Rearrange the equation for initial velocity $v_0$

$v_0=\frac{y - y_0+\frac{1}{2}gt^2}{t}$.
Substitute the values:
\[

$$\begin{align*} v_0&=\frac{-40+\frac{1}{2}\times9.81\times4^2}{4}\\ &=\frac{-40 + \frac{1}{2}\times9.81\times16}{4}\\ &=\frac{-40+78.48}{4}\\ &=\frac{38.48}{4}\\ & = 9.62\approx9.6\text{ m/s} \end{align*}$$

\]

Answer:

9.6 m/s