Question

Jack and Jill are standing on the crate at rest on a frictionless horizontal surface of frozen pond. Jack has a mass of 75.0kg and Jill has a mass of 45.0kg and the crate has a mass of 15.0kg. They remember that they must fetch a pail of water so each umps horizontally from the top of the crate. Just after each jumps, that person is moving away from the crate with the speed of 4.0 m/s relative to the crate. What is the final speed of the crate if both Jack and Jill jump simultaneously and in the same direction? (Use the inertial reference system attached to the ground)

Answer 1

V=4m/s

M=m1+m2=45+75=120kg

By the low of saving energy:

$$m \frac {v ^ {2}}{2} = M \frac {u ^ {2}}{2}$$

where $m = 120\mathrm{kg}$ mass of J&J, $M = 15\mathrm{kg}$ mass of crate, $v = 4\mathrm{m / s}$

u- unknown speed of crate

So we have $u = v\sqrt{m / M} = 4^{*}\sqrt{120 / 15} = 8\sqrt{2} \, \text{m/s}$

Answer $8\sqrt{2} \, \text{m/s}$