Question

A sphere of steel of mass 15 kg moving with a velocity of 12 m/s along X-axis collides with a stationary sphere of mass 20 kg. If velocity of the first sphere after collision is 8 m/s and is moving at an angle of 45° with X-axis, find the magnitude and direction of the second sphere after the collision.

Answer 1

Answer:

V = 6.37 m/s

Angle = - 41.7° with X -axis

Explanation:

A sphere of steel of mass 15 kg moving with a velocity of 12 m/s along X-axis

Momentum before collision = 15 * 12 = 180 along X -axis

= 180 i + 0 j

Momentum after collision =  15 * ( 8 Angle 45)  + 20 ( V Angle α)

= 15 * 8Cos45 i  + 15*8Sin 45 j + 20 * VCosα i +  20 * VSinαj

= ( 60√2 + 20 * VCosα) i + ( 60√2 + 20 * VSinα)j

60√2 + 20 * VSinα = 0

=> VSinα = - 3√2

60√2 + 20 * VCosα = 180

=> 3√2 +  VCosα = 9

=> VCosα = 9 - 3√2

V²Sin²α + V²Cos²α  =  18 + 81 + 18 - 54√2

=> V² = 117 - 54√2

=> V = 6.37 m/s

Angle = - 41.7° with X -axis