Question

A rocket of mass $3\times {10}^{6}kg$ takes off from a launching pad and acquires a vertical velocity of $1km{s}^{-1}$ and an altitude of $25km$. Calculate its (a) potential energy (b) kinetic energy.

Answer 1

Given;

$m=3\times {10}^{6}kg$; mass of the rocket

$g=9.8m{s}^{-2}$; acceleration due to gravity

$h=25km$; height of the rocket from ground

$\Rightarrow h=25000m$

$v=1km{s}^{-1}$; velocity of the rocket

$\Rightarrow v=1000m{s}^{-1}$

(a) Potential energy of the rocket-

$P.E.=mgh$

$\Rightarrow P.E.=3\times {10}^6\times 9.8\times 25000J$

$\Rightarrow P.E.=735\times {10}^{9}J$

(b) Kinetic energy of the rocket-

$K.E=\frac{1}{2}m{v}^2$

$\Rightarrow K.E.=\frac{1}{2}\times 3\times {10}^6\times (1000{)}^{2}J$

$\Rightarrow K.E.=1.5\times {10}^{12}J$