Question

formula 1 point a remote - control car is driven off a hotel balcony at 9 m/s. if it hits the ground 10.4 m from the base of the balcony, then what is the height of the balcony? round to 1 decimal place.

Explanation:

Step1: Find the time of flight

The horizontal motion is a uniform - motion with $v_x = 9\ m/s$ and $x = 10.4\ m$. Using the formula $x=v_x t$, we can solve for $t$.
$t=\frac{x}{v_x}=\frac{10.4}{9}\ s$

Step2: Find the height of the balcony

The vertical motion is a free - fall motion with $a = g=9.8\ m/s^{2}$, $v_{0y}=0\ m/s$. Using the formula $y = v_{0y}t+\frac{1}{2}gt^{2}$, and since $v_{0y} = 0\ m/s$, the formula simplifies to $y=\frac{1}{2}gt^{2}$. Substitute $t=\frac{10.4}{9}\ s$ into the formula.
$y=\frac{1}{2}\times9.8\times(\frac{10.4}{9})^{2}$
$y = \frac{1}{2}\times9.8\times\frac{10.4^{2}}{81}$
$y=\frac{9.8\times108.16}{162}$
$y=\frac{1060.968}{162}\approx6.5\ m$

Answer:

$6.5\ m$