Question

A small object is released from rest and falls 1.00 × 102 feet near the surface of the earth. Neglect air resistance.

How long will it take to fall through the 1.00 × 102 feet mentioned?



3.12 s



4.50 s



2.49 s



6.25 s



10.0 s

Answer 1

Question #36116

A small object is released from rest and falls $1.00 \times 102$ feet near the surface of the earth. Neglect air resistance.

How long will it take to fall through the $1.00 \times 102$ feet mentioned?

3.12 s

4.50 s

2.49 s

6.25 s

10.0 s

Solution:

An object makes the free falling by gravity

The distance travelling on free falling (height) is

$H = H_0 - \frac{1}{2} gt^2$ were $H_0$ is the initial height $g$ is the acceleration due the gravity $t$ is the time

Accepting the final height equal to zero

$$H_0 = \frac{1}{2} gt^2$$ $$t = \sqrt{\frac{2H_0}{g}}$$ $$g = 32.17 \, \text{ft/s}^2$$ $$t = \sqrt{\frac{2 \cdot 1.00 \cdot 10^2}{32.17}} = 2.49 \, \text{sec}$$

Answer: 2.49 sec, (third answer).