Question

A rocket of mass $5\times {10}^5$ kg takes off from a launching pad and acquires a velocity of $2km{s}^{-1}$ at an altitude of $50km$. Calculate (a) the potential energy (b) the kinetic energy. Take $g=10m{s}^{-2}$

Answer 1

Step1: Given that

Mass of the rocket (m) = $5\times {10}^5$ kg

velocity of the rocket (v) = $2km{s}^{-1}$ = $2000m{s}^{-1}$.

height at which the rocket has reached this velocity (h) = $50km$

acceleration due to gravity $g=10m{s}^{-2}$

Step2: Potential Energy (U)

Formula to be used

$U=mgh$

Putting all the values in the above equation, we get

$U=$ $5\times {10}^5$ $\times 10\times 50km$ = $2.5\times {10}^8$ $Joule$

Step3: Kinetic Energy (K.E.)

Formula to be used

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

Putting all the values in the above equation, we get

$K.E=$ $\frac{1}{2}5\times {10}^5\times {\left(2000\right)}^2$ = $1.0\times {10}^{12}Joule$.

Hence, $U=$$2.5\times {10}^8$$Joule$, $K.E=$$1.0\times {10}^{12}Joule$