Question

A body A of mass 1.5kg, travelling along the positive x-axis with speed 4.5m/s, collides with another body B of mass 3.2kg which, initially, is at rest. As a result of the collision, A is deflected and moves with a speed 2.1m/s in a direction which is at angle 30° below the x-axis. B is set in motion at an angle θ above the x-axis. Calculate the velocity of B after the collision

Answer 1

We consider the momentum in the x-direction and apply the principle of conservation of momentum to form the equation:
m(A)u(A) = m(A)v(A) + m(B)v(B), since u(B) = 0 as B is at rest

We calculate v(A) using:
Vx = Vcos∅
Vx = 2.1cos(30)
Vx = 1.82 m/s

1.5 x 4.5 = 1.5 x 1.82 + 3.2v(B)
v(B) = 1.26 m/s

The deflection angle of B will be 30° above the positive x-axis, so:
v(B) = Vcos∅
V = 1.26 / cos(30)
V = 1.45 m/s

The velocity of B is 1.45 m/s