Question

If a Saturn V rocket with an Apollo spacecraft attached had a combined mass of $2.9 \times {10^5}$ kg and reached a speed of 11.2 km/s, how much kinetic energy would it then have?

Answer 1

Hint: In order to solve this kind of numerical we need to know the kinetic energy formula, here the Saturn rocket with an Apollo spacecraft is moving with some velocity V and it contains some mass m attached to it. Hence we can calculate easily by using kinetic energy.

Complete step by step answer:
From the given data
v=11.2km/s
$\implies$ v=$11.2 \times 1000$
$\implies$ v=11200$m{s^{ - 1}}$
m=$2.9 \times {10^5}$kg
The spacecraft which is moving is a part of mechanical energy, because the mechanical energy is the sum of the both energies that is potential and kinetic energy.
The kinetic energy of a mass moving with some constant velocity depends on the mass and the square of the velocity of the mass.
We know that the kinetic energy of a mass m and moving with some velocity v is given by:
 We calculate the kinetic energy,
$\
KE = \dfrac{1}{2}m{v^2} \\
\implies KE = \dfrac{1}{2}(2.9 \times {10^5}){(11200)^2} \\
\therefore KE = 1.8 \times {10^{13}}J \\
\ $

Note:
The kinetic energy is a part of mechanical energy.
The kinetic energy on a mass is due to its velocity or its motion.
Kinetic energy is directly proportional to the mass of the spacecraft and it is square of the velocity of the spacecraft which is moving.