Question

A projectile is moving at 20 m/s at its highest point, where it breaks into equal parts due to an internal explosion. One part moves vertically up at 30 m/s with respect to the ground. Then the other part will move at:
$
  {\text{A}}{\text{. }}20m/s \\
  {\text{B}}{\text{. }}10\sqrt {13} m/s \\
  {\text{C}}{\text{. }}50m/s \\
  {\text{D}}{\text{. }}30m/s \\
 $

Answer 1

Hint: Here we go through by applying the conservation of momentum to find out the velocity of the other part. As we know that the total amount of momentum of the collection of objects in the system is the same before the collision as after the collision.
Formula used: - $\overrightarrow P = m\overrightarrow v $ , where P=momentum, m=mass, v=velocity

Complete Step-by-Step solution:
Here in the question it is given that a projectile is moving at 20 m/s at its highest point.
It means that The system consists of one objects Before the explosion, the total momentum of the system is ‘P=mv’ where the velocity of the particle is given as 20m/s at highest point it means that the vertical speed is zero and it is moving in x direction and let the mass of the particle be m.
So $\overrightarrow {{P_i}} = m \times 20\widehat i$
And after the explosion, the total momentum of the system become,
As in the question it is broken into two equal parts the one part moves vertically up at 30 m/s with respect to the ground and let the velocity of the other part be$\overrightarrow v $.
So $\overrightarrow {{P_f}} = \dfrac{m}{2} \times 30\widehat j + \dfrac{m}{2} \times \overrightarrow v $
Now using momentum conservation,
$\overrightarrow {{P_i}} = \overrightarrow {{P_f}} $
$
   \Rightarrow m \times 20\widehat i = \dfrac{m}{2} \times 30\widehat j + \dfrac{m}{2} \times \overrightarrow v \\
   \Rightarrow \overrightarrow v = 40\widehat i - 30\widehat j \\
 $
We have to give the answer as magnitude so,
$\left| {\overrightarrow v } \right| = \sqrt {{{(40)}^2} + {{( - 30)}^2}} = 50$
Hence option C is the correct answer.

Note: - Whenever we face such a type of question such as explosion or collision we always try to conserve the momentum and assume the unknown velocity and after using momentum conservation we will easily find out the unknown velocity.