Question

A rocket of 3 x 10⁶ kg mass takes off from a launching pad and acquires a vertical velocity of 1 km/s at an altitude of 25 km. Calculate:
(a) the potential energy

Take the value of g = 10 m/s².

Answer 1

Step 1: Given data

Mass of the rocket is, $m=3\times {10}^{6}kg$

Velocity is, $1km/s=1\times {10}^{3}m/s$

Height is, $h=25km=25000m$

Acceleration due to gravity is taken as, $g=10m/s^2$

Step 2: Calculating potential energy

Potential energy is given as,

$PE=mgh$

where, $m$ is mass, $g$ is acceleration due to gravity and $h$ is height.

Substituting the known values in the equation for potential energy, we get,

$$\begin{gathered} PE=\left(3\times {10}^6\right)kg\times 10m/s^2\times 25000m \\ PE=75\times {10}^{10}J \end{gathered}$$

Therefore, the potential energy is $75\times {10}^{10}J$.