Question

1. you drop a ball off the roof of a hotel. it takes the ball 19 seconds to reach the ground.

a. how tall is the hotel?
b. what was the balls final velocity just as it reached the ground?

1. you jump in the air and reach a max height of 6m. if you jump with a velocity of 1.8m/s, how long are you in the air for?

Explanation:

Problem 8a:

Step1: Select free-fall displacement formula

Use $h = \frac{1}{2}gt^2$, where $g=9.8\,\text{m/s}^2$, $t=19\,\text{s}$

Step2: Substitute values and calculate

$h = \frac{1}{2} \times 9.8 \times 19^2 = 4.9 \times 361$

Problem 8b:

Step1: Select free-fall velocity formula

Use $v = gt$, where $g=9.8\,\text{m/s}^2$, $t=19\,\text{s}$

Step2: Substitute values and calculate

$v = 9.8 \times 19$

Problem 9:

Step1: Time to reach max height

Use $t_1 = \frac{v_0}{g}$, where $v_0=1.8\,\text{m/s}$, $g=9.8\,\text{m/s}^2$
$t_1 = \frac{1.8}{9.8}$

Step2: Time to fall from max height

Use $t_2 = \sqrt{\frac{2h}{g}}$, where $h=6\,\text{m}$, $g=9.8\,\text{m/s}^2$
$t_2 = \sqrt{\frac{2 \times 6}{9.8}} = \sqrt{\frac{12}{9.8}}$

Step3: Total air time

$t_{\text{total}} = t_1 + t_2$

Answer:

8a. $1768.9\,\text{meters}$
8b. $186.2\,\text{m/s}$

1. $\approx 1.31\,\text{seconds}$