Question

two objects of 10kg and 8kg are moving on a straight road with a velocity of 20m/s and 15m/s respectively. if the second object moves with 25m/s after collision calculate the velocity of first object.
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Answer 1

Let,

Object 1 = A

Object 2 = B

Given :-

Mass of A (m₁) = 10kg

Initial velocity of A (u₁) = 20m/s

Mass of B (m₂) = 8kg

Initial velocity of B (u₂) = 15m/s  

After collision,

Final velocity of B (v₁) = 25m/s

Final velocity of A (v₂) = ?

Solution :-

Momentum before collision

= Initial Momentum of A + Initial Momentum of B

= m₁u₁ + m₂u₂

= 10(20) + 8(15)

= 200 + 120

= 320

Momentum after collision

= Final Momentum of A + Final Momentum of B

= m₁v₁ + m₂v₂

= 10(v₁) + 8(25)

= 10v₁ + 200

According to the Law of Conservation of Momentum, the total momentum before collision is equal to the total momentum after collision.

∴ m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂

320 = 10v₁ + 200

320 - 200 = 10v₁

120 = 10v₁

v₁ = 120/10

v₁ = 12

∴ Velocity of first object after collision is 12m/s.