4. A physicist of mass 59kg is stuck in the middle of a frictionless ice sheet.

Question

4. A physicist of mass 59kg is stuck in the middle of a frictionless ice sheet. She decides to throw both of her identical mittens (each of mass 0.35kg) to give herself some velocity to move off the ice. She is capable of throwing them with a maximum speed of 2.5. In order to get off the ice as quickly as possible, should she throw both mittens at the same time, or one right after the other? (Assume she would throw the two mittens together at 2.5m, and she would throw each mitten individually at 2.5) Justify your answer by doing appropriate calculations. (The calculations are required for credit.)

Explanation / Answer

a) Throwing two mittens at the same time.
Consider the mass of mittens as m and the throwing velocity as v. Consider the mass of physicist as M and her velocity after the throw as V
Using conservation of momentum,
2mv = (M - 2m)V
V = 2mv/(M - 2m)
= (2 x 0.35 x 2.5) / (59 - 2 x 0.35)
= 0.03002 m/s

b) Throwing one mitten after the other.
After throwing the first mitten, her velocity become,
V = mv/(M - m)
= (0.35 x 2.5) / (59 - 0.35)
= 0.01491 m/s
When she is moving with 0.015 m/s velocity, she throws the next mitten

Consider that her center of mass is moving with the velocity 0.015 m/s
Her final velocity with center of mass is,
V = mv/(M - 2m)
= (0.35 x 2.5) / (59 - 2 x 0.35)
= 0.0150086 m/s

Final velocity with respect to ground = 0.01491 + 0.0150086 = 0.2993 m/s

Since throwing two mittens at the same time has more initial velocity, it is preferred.

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