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26 October, 15:03

A wagon is rolling forward on level ground. Friction is negligible. The person sitting in the wagon is holding a rock. The total mass of the wagon, rider, and rock is 95.8 kg. The mass of the rock is 0.325 kg. Initially the wagon is rolling forward at a speed of 0.530 m/s. Then the person throws the rock with a speed of 15.1 m/s. Both speeds are relative to the ground. Find the speed of the wagon after the rock is thrown (a) directly forward in one case and (b) directly backward in another.

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  1. 26 October, 17:34
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    a) 0.48 m/s

    b) 0.583 m/s

    Explanation:

    As the wagon rolls,

    momentum'p' = m x v = > 95.8 x 0.530 = 50.774 Kgm/s

    (a) Rock is thrown forward,

    momentum of rock = 0.325 x 15.1 = 4.9075 Kgm/s

    Conservation of momentum says momentum of wagon is given by

    50.774 - 4.9075 = 45.8665

    Therefore, Speed of wagon = 45.8665 / (95.8-0.325) = 0.48 m/s

    (b) Rock is thrown backward,

    momentum of wagon = 50.774 + 4.9075 = 55.68 Kgm/s

    Therefore, speed of wagon = 55.68 / (95.8-0.325) = 0.583 m/s
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