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8.85: a) If the crate had final speed v , J&J have speed 4.00 m s − v relative to the ice,<br />

(120.0 kg) (4.00 m s)<br />

and so ( 15.0 kg) v = (120.0 kg)(4.00 m/s − v).<br />

Solving for v v =<br />

= 3.56m s.<br />

,<br />

(135.0 kg)<br />

(75.0 kg)<br />

b) After Jack jumps, the speed of the crate is (4.00m s) = 2.222m s,<br />

and the<br />

(135.0 kg)<br />

momentum of Jill and the crate is 133.3 kg ⋅ m s . After Jill jumps, the crate has a speed v<br />

and Jill has speed 4.00 m s − v,<br />

and so<br />

133 .3 kg ⋅ m s = (15.0 kg) v − ( 45.0 kg)(4.00 m s − v),<br />

and solving for v gives<br />

v = 5.22 m s. c) Repeating the calculation for part (b) with Jill jumping first gives a final<br />

speed of 4 .67 m s.

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