Question

Janet is skating at the ice rink with her little sister Sarah who is initially standing at rest on the ice. Janet then collides head-on into Sarah. Janet continues forward at 2 m/S, while Sarah is thrown backward at 4 m/s. (After the collision, Janet and Sarah are moving in the same direction). Janet's mass is 58 kg and Sarah's mass is 39 kg. How fast was Janet moving initially, in m/s? (Round your answer to one decimal place if necessary.)

Answer 1

Answer: According to the law of conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision. Assuming that the positive direction is the direction in which Janet was moving before the collision, we can write:

Initial momentum = final momentum

(mass of Janet) x (initial velocity of Janet) + (mass of Sarah) x (initial velocity of Sarah) = (mass of Janet) x (final velocity of Janet) + (mass of Sarah) x (final velocity of Sarah)

We know that Sarah was initially at rest, so her initial velocity was 0 m/s. We also know that Janet continued forward at 2 m/s after the collision, so her final velocity was 2 m/s. Substituting these values into the equation above and solving for the initial velocity of Janet, we get:

(58 kg) x (initial velocity of Janet) + (39 kg) x (0 m/s) = (58 kg) x (2 m/s) + (39 kg) x (4 m/s)

58(initial velocity of Janet) = 406 + 156

58(initial velocity of Janet) = 562

(initial velocity of Janet) = 9.69 m/s (rounded to two decimal places)

Therefore, Janet was moving at 9.69 m/s initially before the collision.

Step-by-step explanation: