Question

A rocket of mass $3\times {10}^{6}kg$ takes off from a launching pad and acquires a vertical velocity of $1km{s}^{-1}$ at an altitude of $25km$. The kinetic energy of the rocket is: [ Take $g=10m{s}^{-2}$]

• A. $1.5\times {10}^{11}J$
• B. $1.5\times {10}^{12}J$
• C. $1.5\times {10}^{10}J$
• D. none of the above

Answer 1

The correct option is B

$1.5\times {10}^{12}J$

Step 1: Given data:

Mass, $m=3\times {10}^{6}kg$

Vertical velocity, $v=1km{s}^{-1}={10}^{3}m{s}^{-1}$

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

Height, $h=25km=25000m$

Kinetic energy, $K.E.=?$ ( To be calculated)

Step 2: Calculating the kinetic energy

$$\begin{gathered} KineticEnergy(K.E.)=\frac{1}{2}\times m\times v^2 \\ \Rightarrow K.E.=\frac{1}{2}\times 3\times {10}^{6}kg\times {(1\times {10}^3)}^{2}m{s}^{-1} \\ \Rightarrow K.E.=1.5\times {10}^{12}J \end{gathered}$$

Therefore, the kinetic energy of the rocket is $1.5\times {10}^{12}J$

Hence, the correct answer is an option (B) i.e. $1.5\times {10}^{12}J$