an arrow of mass m is shot horizontally at speed v. the arrow passes through the center of mass of melon with mass M. calculate the speed of

Question

an arrow of mass m is shot horizontally at speed v. the arrow passes through the center of mass of melon with mass M. calculate the speed of the arrow-melon system just after the arrow sticks in the melon

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bonexptip 5 years 2021-07-26T14:59:05+00:00 1 Answers 23 views 0

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  1. mit
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    2021-07-26T15:00:43+00:00
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    Answer:

    The final velocity of the melon-arrow system immediately after collision is:

    v_f=\frac{m*v}{(m+M)}

    Explanation:

    We use conservation of momentum to solve this problem.

    The initial state consists of an arrow of mass m and speed v , and a static melon that is not moving (velocity = 0)

    Therefore, the initial momentum P_i of the system which is the addition of the initial momentum of the arrow (p_{ai}) plus the initial momentum of the melon (p_{mi} is;

    P_i = p_{ai}+p_{mi}\\P_i=m*v+M*0\\P_i=m*v

    The final system consists of the arrow stack to the melon (total mass “m+M”), travelling at the unknown velocity v_f that we need to find. The final momentum of this system is therefore the product of this mass times the unknown velocity:

    P_f=(m+M)*v_f

    Due to conservation of momentum in this inelastic collision, we set the equation that equals the system’s initial momentum to the final momentum, and solve for the unknown velocity:

    P_i=P_f\\m*v=(m+M)*v_f\\v_f=\frac{m*v}{(m+M)}

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