Question

A machine gun fires 240 bullets per minute. If the mass of each bullet is 10 g and find out the velocity of the bullets, if the power of the gun is 7.2kW.

Answer 1

Hint
Velocity is defined as the rate change of displacement per unit time. Speed in a specific direction is also known as velocity. Velocity is equal to displacement divided by time. Velocity measures the movement of objects based on their speed and direction.

Complete step by step answer
According to the question the number of bullets is $N = 240$.
And, the power is $P = 7.2 kw$
According to the formula power (P) = $\dfrac{W}{t}$
W= work done, upon time = t.
According to the question work done is equal to kinetic energy of the bullets-
So, $P = \dfrac{{N{{(\Delta K.E)}_{bullet}}}}{t}$
Or, $P = \dfrac{{N \times \dfrac{1}{2} \times m{v^2}}}{t}$
Put the values that we know according to the question,
$
  7.2 = \dfrac{{240 \times \dfrac{1}{2} \times 10{v^2}}}{{60}} \\
   \Rightarrow {v^2} = \dfrac{{7.2 \times 60}}{{240 \times 10}} \\
 $
$
   \Rightarrow {v^2} = 0.36 \\
   \Rightarrow v = \sqrt {0.36} \\
 $
$\therefore v = 0.6 \times {10^3} = 600m{s^{ - 1}}$.

Note
Kinetic energy is the energy of mass in motion. The kinetic energy of an object is the energy it has because of its motion. Note that energy is a scalar quantity, i.e., it does not depend on direction, and it is always positive.