Chapter 4, Problem 56A

Kenny Klutz drops his physics book off his aunt’s high-rise balcony. It hits the ground below 1.5 s later.

a. With what speed does it

b. How high is the balcony? Ignore air drag.

To determine

The speed with which the physics book hits the ground below $1.5\text{s}$ later.

Answer to Problem 56A

  $15\text{m/s}$

Explanation of Solution

Given:

The time taken, $t=1.5\text{s}$

Formula used:

The instantaneous speed in free fall at a time $t$ is given by,

  $v=at$

where, $a=g=10{\text{m/s}}^{\text{2}}$ = acceleration of free fall

Calculation:

Using the above mentioned formula and given value, the speed with which the physics book hit the ground below will be,

  $\begin{array}{c}v=\left(10\right)\left(1.5\right)\\ =15\text{m/s}\end{array}$

Conclusion:

Hence, the speed with which the physics book hits the ground below is $15\text{m/s}$ .

To determine

The height of the balcony above the ground.

Answer to Problem 56A

  $11.25\text{m}$

Explanation of Solution

Given:

The time taken, $t=1.5\text{s}$

Formula used:

The distance covered in free fall in a time $t$ is given by,

  $d=\frac{1}{2}a{t}^2$

where, $a=g=10{\text{m/s}}^{\text{2}}$ = acceleration of free fall

Calculation:

Using the above mentioned formula and given value, the height of the balcony above the ground will be,

  $\begin{array}{c}d=\frac{1}{2}\left(10\right){\left(1.5\right)}^2\\ =11.25\text{m}\end{array}$

Conclusion:

Hence, the height of the balcony is $11.25\text{m}$ .