Chapter 2.1, Problem 64E

Solution

To Determine:

The initial vertical velocity required to attain a maximum height of $48\text{ ft}$ .

The initial vertical velocity of approximately $55.43\text{ ft/sec}$ is required to attain a maximum height of $48\text{ ft}$ .

Given:

Initial height of water drop is zero.

Maximum height to attain is $48\text{ ft}$ .

Concepts Used:

The maximum height $h_{\text{max}}$ of an object in free fall motion is related to the initial vertical velocity of launch from ground $v_0$ by the equation $v_0=\sqrt{2g{h}_{\text{max}}}$ , where $g=32{\text{ ft/sec}}^2$ is the acceleration due to gravity.

Calculations:

Substitute the values of maximum height $h_{\text{max}}=48\text{ ft}$ , and the acceleration due to gravity $g\approx 32{\text{ ft/sec}}^2$ in the equation $v_0=\sqrt{2g{h}_{\text{max}}}$ and determine the required initial vertical velocity $v_0$ :

  $\begin{array}{c}{v}_0=\sqrt{2g{h}_{\text{max}}}\\ =\sqrt{2\times 32\times 48}\\ \approx 55.43\end{array}$

Conclusion:

The initial vertical velocity of approximately $55.43\text{ ft/sec}$ is required to attain a maximum height of $48\text{ ft}$ .