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
(b) the kinetic 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, $v=1km/s=1\times {10}^{3}m/s$

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

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

Step 2: Calculating kinetic energy

Kinetic energy is given as,

$KE=\frac{1}{2}m{v}^2$

where, $m$ is mass and $v$ is velocity.

On substituting the known values in the above equation,

$$\begin{gathered} KE=\frac{1}{2}\times \left(3\times {10}^6\right)kg\times {\left({10}^{3}m/s\right)}^2 \\ KE=1.5\times {10}^{12}J \end{gathered}$$

Therefore, kinetic energy is $1.5\times {10}^{12}J$.