Question

A sticky ball of mass 0.0450 kg, traveling with a speed of 22.0 m/s in a direction 30.00 below the +x axis collides with another moving ball, of mass 0.0119 kg, traveling in a direction 44.70 above the +x axis. The two balls stick together and keep moving horizontally. The initial speed of the second ball is:

a) 59.1 m/s

b) 18.9 m/s

c) 75.7 m/s

d) 30.2 m/s

e) 42.6 m/s

Answer 1

Mass of the first ball = m₁ = 0.045 kg

Mass of the second ball = m₂ = 0.0119 kg

Initial velocity of the first ball = V₁ = 22 m/s

Direction of the initial velocity of the first ball = ₁ = 30^o below the positive X-axis

Y-component of initial velocity of the first ball = V_1y = -V₁Sin₁ (Negative as it is directed along negative Y-axis)

Initial velocity of the second ball = V₂

Direction of the initial velocity of the second ball = ₂ = 44.7^o above the positive X-axis

Y-component of initial velocity of the second ball = V_2y = V₂Sin₂

After the collision both the balls stick to each other and move in the horizontal direction therefore the final momentum of the system in the Y-direction is zero.

By conservation of linear momentum in Y-direction,

V₂ = 59.1 m/s

Initial speed of the second ball = 59.1 m/s