Question

Use the following information for question 26 and 27. A 550-g ball traveling at 8.0 m/s undergoes a sudden head-on perfectly 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

Answer 1

Answer:

The speed of 250 g ball after collision is 14 m/s.

Explanation:

mass of first ball, m = 550 g = 0.55 kg

initial velocity of first ball,  u = 8 m/s

mass of second ball, m' = 250 g = 0.25 kg

initial velocity of second ball, u' = - 8 m/s

Let the speed of the balls is v and v' after the collision.

Use conservation of momentum

m u + m' u' = m v + m' v'

0.55 x 8 - 0.25 x 8 = 0.55 v + 0.25 v'

0.55 v + 0.25 v' = 2.4 ..... (1)

Use the formula  of coefficient of restitution,

For elastic collision, e = 1

$e =\frac{v'-v}{u - u'}\\\\1 =\frac{v'-v}{8+8}\\\\16 =v' - v...... (2)$

By solving (1) and (2)

v = - 2 m/s and v' = 14 m/s