Question

a small, private airplane is carrying three passengers to an island. the plane is 0.9 km in the air. if the potential energy of the plane and its three passengers is 48,510,000 j, what is the combined mass of the plane and its passengers? round your answer to the tenth place.

Explanation:

Step1: Recall potential - energy formula

The formula for gravitational potential energy is $U = mgh$, where $U$ is potential energy, $m$ is mass, $g$ is the acceleration due to gravity ($g= 9.8\ m/s^{2}$), and $h$ is height. We are given $U = 48510000\ J$ and $h=0.9\ km = 900\ m$.

Step2: Solve for mass $m$

Rearrange the formula $U = mgh$ to $m=\frac{U}{gh}$. Substitute $U = 48510000\ J$, $g = 9.8\ m/s^{2}$, and $h = 900\ m$ into the formula.
$m=\frac{48510000}{9.8\times900}$
$m=\frac{48510000}{8820}$
$m = 5500\ kg$

Answer:

$5500.0\ kg$