A 5.0-kg ball and a 10.0-kg ball approach each other with equal speeds of 20 m/s.If they collide inelastically,the speed of the balls just after the collision is approximately
A)1.0 m/s
B)20 m/s
C)6.7 m/s
D)1.5 m/s
E)zero

Question

Quizplus · Accepted Answer

The momentum before the collision is given by: 
p = mv1 + mv2 = 5 kg x 20 m/s + 10 kg x (-20 m/s) = 0

Since momentum is conserved in an inelastic collision, the final momentum of the system must also be zero. Therefore, the balls will stick together and move with a common velocity.

Using the conservation of energy, we can find the final velocity v: 
1/2 m1v1^2 + 1/2 m2v2^2 = 1/2 (m1 + m2) v^2 
v = sqrt[(m1v1^2 + m2v2^2)/(m1 + m2)] 
v = sqrt[(5 kg x (20 m/s)^2 + 10 kg x (20 m/s)^2)/(5 kg + 10 kg)] 
v ≈ 6.7 m/s

Therefore, the correct answer is (C) 6.7 m/s.

A 50-Kg Ball and a 10