Question

A truck of mass 2500 kg moving at 15 m/s collides with a car of mass 1000 kg moving at 5 m/s in the opposite direction. With what velocity would they move if they got jammed to each other ?

Answer 1

according to conservation of momentum,
m1v1+m2v2=(m1+m2)v
2500×15+1000×(-5)=3500×v
-ve sign is for opposite direction
v=32500÷3500
=9.8m/s

Answer 2

They would move with velocity of 9.29 m/s if they got jammed to each other.

Explanation

❐ A truck of mass 2500 kg moving at 15 m/s collides with a car of mass 1000 kg moving at 5 m/s in the opposite direction.

❐ With what velocity would they move if they got jammed to each other ?

Solution

From the question we have ; mass of 1st truck (m₁) = 2500 kg. Initial velocity of 1st truck (u₁) = 15 m/s.

Mass of 2nd truck (m₂) = 1000 kg. Initial velocity of 2nd truck (u₂) = 5 m/s.

According to law of conservation of momentum :

❐ m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂

Now as two trucks will collide with each other, so final velocity of both trucks would be same i.e. v₁ = v₂ = v

And, as the 2nd truck is moving in the opposite direction, so initial velocity of 2nd truck i.e. u₂ would be in negative i.e. (-5) m/s

Now substuting values,

➻ (2500 × 15) + 1000 × (-5) = v(2500 + 1000)

➻ 37500 - 5000 = v(3500)

➻ 32500 = 3500v

➻ v = 32500/3500

➻ v = 9.29 m/s

Therefore, they will move with velocity of 9.29 m/s if they got jammed to each other.