During a football game, a receiver has just caught a pass and is standing still. Before he can move, a tackler, running at a velocity of 3.

Question

During a football game, a receiver has just caught a pass and is standing still. Before he can move, a tackler, running at a velocity of 3.8 m/s, grabs and holds onto him so that they move off together with a velocity of 2.3 m/s. If the mass of the tackler is 130 kg, determine the mass of the receiver in kilograms. Assume momentum is conserved.

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Thành Công 3 months 2021-08-09T12:41:13+00:00 1 Answers 5 views 0

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    2021-08-09T12:42:54+00:00

    Answer:

    The mass of the receiver is 85 kg.

    Explanation:

    Given:

    Mass of the tackler (M) = 130 kg

    Mass of the receiver = ‘m’ (Assume)

    Initial velocity of the receiver (u) = 0 m/s

    Initial velocity of the tackler (U) = 3.8 m/s

    Final combined velocity (v) = 2.3 m/s

    So, as per question, the momentum is conserved. Therefore, the total initial momentum is equal to the total final momentum.

    Total initial momentum is given as:

    P_i=mu+MU\\\\P_i=0+130\times 3.8\\\\P_i=494\ kg\cdot m/s

    Total final momentum is given as:

    P_f=(m+M)v\\\\P_f=(m+130)2.3

    Now, as per momentum conservation:

    P_f=P_i\\\\(m+130)2.3=494\\\\m+130=\frac{494}{2.3}\\\\m=214.78-130\\\\m=84.78\ kg\approx85\ kg

    Therefore, the mass of the receiver is 85 kg.

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