Question

Two cars collide with each other. The initial speeds are 3 m / s and 2 m / s. Their respective masses are 100kg and 90kg. What will be the car speed of 90kg after the collision.

Answer 1

m₁ = mass of first car = 100 kg

v_1i = initial velocity of first car = 3 m/s

v_1f = final velocity of first car = ?

m₂ = mass of second car = 90 kg

v_2i = initial velocity of second car = 2 m/s

v_2f = final velocity of second car = ?

Using conservation of momentum

m₁ v_1i + m₂ v_2i = m₁ v_1f + m₂ v_2f

(100) (3) + (90) (2) = (100) v_1f + (90) v_2f

(100) v_1f + (90) v_2f = 480

v_2f = (48 - 9 v_2f )/10                                                                    Eq-1

Using conservation of kinetic energy

m₁ v²_1i + m₂ v²_2i = m₁ v²_1f + m₂ v²_2f

(100) (3)² + (90) (2)² = (100) v²_1f + (90) v²_2f

Using eq-1

(100) (3)² + (90) (2)² = (100) v²_1f + (90) ((48 - 9 v_2f )/10)²

v_1f = 1.66 m/s

Using eq-1

v_2f = (48 - 9 v_2f )/10

v_2f = (48 - 9 (1.66))/10

v_2f = 3.31 m/s