Question

clara dropped a palm fruit to the ground from the top of a tree 45 m tall. how long does it take for the fruit to reach the ground? ($g = 10\\ \text{m/s}^2$).

Explanation:

Step1: Select free-fall displacement formula

The vertical displacement of a freely falling object (starting from rest) is given by:
$$h = \frac{1}{2}gt^2$$
where $h=45\ \text{m}$, $g=10\ \text{m/s}^2$, and $t$ is the time we need to find.

Step2: Rearrange formula to solve for $t$

Isolate $t$ by first multiplying both sides by 2:
$$2h = gt^2$$
Then divide both sides by $g$:
$$t^2 = \frac{2h}{g}$$
Take the square root of both sides:
$$t = \sqrt{\frac{2h}{g}}$$

Step3: Substitute values and calculate

Substitute $h=45$ and $g=10$ into the formula:
$$t = \sqrt{\frac{2\times45}{10}} = \sqrt{\frac{90}{10}} = \sqrt{9}$$

Answer:

$3$ seconds