Question

§. If a red ball with a mass of 10 kg is traveling east at a speed of 5 m/s and collides with a blue ball with a mass of 20 kg traveling west at a speed of 10 m/s if the 20 kg blue ball continues to the west at 2.5 m/s, what is the velocity of the 10 kg red

ball?

Answer 1

Before the collision, the momentum of the red ball is:

p1 = m1v1 = (10 kg)(5 m/s) = 50 kg⋅m/s east

Before the collision, the momentum of the blue ball is:

p2 = m2v2 = (20 kg)(-10 m/s) = -200 kg⋅m/s west

Since there is no external force acting on the system of the two balls, the total momentum is conserved:

p1 + p2 = (m1 + m2)vf

where vf is the final velocity of the combined balls.

Substituting the values we have:

50 kg⋅m/s - 200 kg⋅m/s = (10 kg + 20 kg)vf

-150 kg⋅m/s = 30 kg vf

vf = -5 m/s

Therefore, the velocity of the combined balls after the collision is 5 m/s to the west.

To find the velocity of the red ball after the collision, we can use the fact that momentum is conserved in the direction of the collision:

m1v1 + m2v2 = (m1 + m2)vf

Substituting the values we have:

(10 kg)(5 m/s) + (20 kg)(-10 m/s) = (10 kg + 20 kg)(-5 m/s + vr)

50 kg⋅m/s - 200 kg⋅m/s = 30 kg (-5 m/s + vr)

-150 kg⋅m/s = -150 kg⋅m/s + 30 kg vr

vr = 0 m/s

Therefore, the velocity of the red ball after the collision is 0 m/s (it comes to a stop).

Step-by-step explanation:

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