# Question #66118

Sep 29, 2015

I found $1.3 m$

#### Explanation:

I tried this:

Sep 30, 2015

It's 1.3 meters, correct to 1 decimal place.

#### Explanation:

Assuming no air resistance, use the formula ${v}^{2} = {u}^{2} - 2 a s$ where $v$ is the final velocity, which is $0$ since the coin is at rest in its maximum vertical displacement, $u$ is the initial velocity, which is $5$, $a$ is the acceleration due to gravity and $s$ is the displacement of the coin.

So, inputting the values into the formula, you get:
${0}^{2} = {5}^{2} - 2 \cdot 9.81 \cdot s$
(The reason I'm using a $-$ before $2 a s$ is because the coin is moving upwards, hence it is acting against gravity, so the value of $a$ is negative. The original formula is ${v}^{2} = {u}^{2} + 2 a s$, and since $a$ is negative, I've incorporated a $-$ to make the calculations simpler.)

$0 = 25 - 19.62 s$
$0 + 19.62 s = 25 - 19.62 s + 19.62 s$
$19.62 s = 25$
$s = \frac{25}{19.62}$
$s = 1.27$
$s \approx 1.3 m$