A 550-g ball traveling at 8.0 m/s undergoes a sudden head-on elastic collision with a 250-g ball traveling toward it also at 8.0 m/s. What is the speed of the 250 -g mass just after the collision?
A) 4.0 m/s
B) 8.0 m/s
C) 15 m/s
D) 0 m/s
E) 14 m/s

Question

A  550-g ball traveling at  8.0 m/s undergoes a sudden head-on elastic collision with a  250-g ball traveling toward it also at  8.0 m/s. What is the speed of the 250 -g mass just after the collision?
A)  4.0 m/s
B)  8.0 m/s
C)  15 m/s
D)  0 m/s
E)  14 m/s

Quizplus · Accepted Answer

In an elastic collision, both momentum and kinetic energy are conserved. The formula for the final velocity of the second object (v2') in a one-dimensional elastic collision is given by v2' = [(2m1)/(m1 + m2)]v1 + [(m2 - m1)/(m1 + m2)]v2, where m1 and m2 are the masses of the two objects, and v1 and v2 are their initial velocities, respectively. Plugging in the given values (m1 = 550g = 0.55kg, m2 = 250g = 0.25kg, v1 = 8.0m/s, v2 = -8.0m/s (since it's moving toward the first ball)), we get v2' = [(2*0.55)/(0.55 + 0.25)]*8 + [(0.25 - 0.55)/(0.55 + 0.25)]*(-8) = 14 m/s.

A 550-G Ball Traveling at 8