Question

Two equal masses collide in space away from any gravitational object. Mass A is moving in a straight line at 45 m/s and mass B is initially at rest. After the collision mass A is traveling along a path that makes a +30o angle with its initial direction of motion, and mass B is traveling at an angle of -45o relative to A's initial motion. (a) Find the speeds of the two masses after the collision. (b) What is the change in kinetic energy of the system because of the collision?

Answer 1

Given is:-

mass of the both objects = m kg

Initial velocity of A is u₁= 45m/s

Initial velocity of B is u₂ = 0

Angle of A after the collision  

Angle of B aftet the collision  

Now,

part-a

Let the speeds of A & B after collison is v₁ and v₂ respectively

THus by applying conservation of momentum in x direction we get

by plugging all the values we get

eq-1

and in y direction

by eliminating m and plugging values we get

or

which gives

by plugging this value in eq-1 we get

which gives

and

Part-b

Initial kinetic energy of the system

Joules

final energy of the system is

Joules

Thus the change in the kinetic energy of the system is

joules

Hence the change in the kinetic energy of the system is negative therefore there is energy loss in the collision