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12 June, 02:04

A grocery shopper tosses a (n) 8.1 kg bag of rice into a stationary 18.2 kg grocery cart. The bag hits the cart with a horizontal speed of 6.9 m/s toward the front of the cart. What is the final speed of the cart and bag?

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  1. 12 June, 05:52
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    2.125 m/s

    Explanation:

    From the law of conservation of momentum,

    Total momentum before collision = Total momentum after collision.

    Note: Assuming a inelastic collision occur between the grocery cart and the bag.

    mv+m'v' = V (m+m') ... Equation 1

    Where m = mass of the cart, m' = mass of the bag, v = initial velocity of the grocery cart, v' = final velocity of the bag, V = Final velocity of the bag and the cart.

    Making V the subject of the equation,

    V = (mv+m'v') / (m+m') ... Equation 2

    Given: m = 18.2 kg, m' = 8.1 kg, v' = 6.9 m/s, v = 0 m/s (stationary)

    Substitute into equation 2

    V = [ (18.2*0) + (8.1*6.9) ] / (8.1+18.2)

    V = 55.89/26.3

    V = 2.125 m/s.

    Hence the final speed of the cart and the bag = 2.125 m/s
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