A truck of mass $500 k g$ moving at $4 m s^{- 1}$ collides with another truck of mass $1500 k g$ moving in the same direction at $2 m s^{- 1}$ .What is their common velocity just after the collision if they move off together?

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Solution

Step 1: Given data
Mass of the first truck, $m_{1} = 500 k g$
The velocity of truck, $v_{1} = 4 m s^{- 1}$
Mass of second truck, $m_{2} = 1500 k g$
Velocity of second truck, $v_{2} = 2 m s^{- 1}$
Combined mass, $m = 1500 k g + 500 k g = 2000 k g$
Let the common velocity be $v$ after the collision.

Step 2: Calculation of final velocity after the collision
According to the law of conservation of momentum
initial momentum = final momentum
$m_{1} v_{1} + m_{2} v_{2} = m v 500 k g \times 4 m s^{- 1} + 1500 k g \times 2 m s^{- 1} = (1500 + 500) v \Rightarrow 2000 v = 2000 + 3000 \Rightarrow 2000 v = 5000 \Rightarrow v = \frac{5000}{2000} \Rightarrow v = 2.5 m s^{- 1}$
Hence, their common velocity just after collision is $2.5 m s^{- 1}$ .

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A truck of mass 500kg moving at 4ms-1 collides with another truck of mass 1500kg moving in the same direction at 2ms-1.What is their common velocity just after the collision if they move off together?

A truck of mass $500 k g$ moving at $4 m s^{- 1}$ collides with another truck of mass $1500 k g$ moving in the same direction at $2 m s^{- 1}$ .What is their common velocity just after the collision if they move off together?