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29 July, 13:24

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 93.5 kg. The mass of the rock is 0.310 kg. Initially the wagon is rolling forward at a speed of 0.540 m/s. Then the person throws the rock with a speed of 16.5 m/s. Both speeds are relative to the ground. Find the speed of the wagon after the rock is thrown directly forward.

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  1. 29 July, 13:38
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    Given Data

    Total mass=93.5 kg

    Rock mass=0.310 kg

    Initially wagon speed=0.540 m/s

    rock speed=16.5 m/s

    To Find

    The speed of the wagon

    Solution

    As the wagon rolls, momentum is given as

    P=mv

    where

    m is mass

    v is speed

    put the values

    P=93.5kg * 0.540 m/s

    P = 50.49 kg*m/s

    Now we have to find the momentum of rock

    momentum of rock = mv

    momentum of rock = (0.310kg) * (16.5 m/s)

    momentum of rock = 5.115 kg*m/s

    From the conservation of momentum we can find the wagons momentum So

    wagon momentum=50.49 - 5.115 = 45.375 kg*m/s

    Speed of wagon = wagon momentum / (total mass-rock mass)

    Speed of wagon=45.375 / (93.5-0.310)

    Speed of wagon = 0.487 m/s

    Throwing rock backward,

    momentum of wagon = 50.49+5.115 = 55.605 kg*m/s

    Speed of wagon = wagon momentum / (total mass-rock mass)

    speed of wagon = 55.605 kg*m/s / (93.5kg-0.310kg)

    speed of wagon = 0.5967 m/s
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