Two billiard balls undergo a glancing collision.Before the collision the first ball was travelling east at 2.6 m/s and the second ball was travelling west at 1.2 m/s.If the second ball is deflected by +90 degrees travelling north at 1.47 m/s,what is the speed of the first ball after the collision?
A)1.39 m/s
B)1.68 m/s
C)2.57 m/s
D)2.03 m/s

Question

Quizplus · Accepted Answer

We can use conservation of momentum in the x and y directions to solve for the velocity of the first ball after the collision.
In the x direction, the momentum before the collision is:
p_before = m1*v1 + m2*(-v2)
where m1 and m2 are the masses of the balls and v1 and v2 are their velocities.
After the collision, since the first ball continues to travel in the same direction, the momentum in the x direction is conserved:
p_after_x = m1*v1_after + m2*(-v2_after)
where v1_after is the velocity of the first ball after the collision and v2_after is the velocity of the second ball after the collision in the x direction. Since the second ball is deflected by 90 degrees, its velocity in the x direction is 0.
So we have:
p_before = p_after_x
m1*v1 + m2*(-v2) = m1*v1_after
Solving for v1_after, we get:
v1_after = (m1*v1 + m2*(-v2))/m1
v1_after = (1*2.6 - 1*(-1.2))/1 = 3.8/1 = 3.8 m/s
In the y direction, the momentum before the collision is 0, and after the collision, momentum is conserved:
p_after_y = m2*v2_after
where v2_after is the velocity of the second ball after the collision in the y direction (north). So we have:
m2*(-v2) = m2*v2_after
Solving for v2_after, we get:
v2_after = (-1.2)/(m2/m2) = -1.2 m/s
Note that the negative sign indicates that the second ball is moving in the negative y direction (south) after the collision. Taking the magnitude of the velocity, we get:
|v2_after| = 1.47 m/s
So the speed of the first ball after the collision is the magnitude of its velocity:
|v1_after| = 3.8 m/s
Therefore, the answer is D) 2.03 m/s, which is the magnitude of the velocity of the first ball after the collision rounded to two significant figures.

Two Billiard Balls Undergo a Glancing Collision