The recoil speed of the catapult is 6.96 m/s.
The rate at which a body's displacement changes in relation to time is known as its velocity. Velocity is a vector quantity with both magnitude and direction. SI unit of velocity is meter/second.
Given parameters:
Mass of the catapult : M = 1400 kg.
Mass of the boulder: m = 75 kg.
Velocity of the rock: v = 130 m/s.
We have to find: recoil speed of the catapult: V = ?
From the principle of conservation of linear momentum:
momentum of the boulder = - momentum of the catapult
⇒ mv = - MV
⇒ v = -mv/M = - (75 × 130)/1400 m/s = - 6.96 m/s
Negative sign indicates recoil of the catapult is in opposite direction of motion of the boulder.
So, the recoil speed of the catapult is 6.96 m/s.
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