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2 May, 13:07

An archer draws his compound bow and shoots an arrow. The 23 g arrow leaves the bow with a velocity of 88 m/s. The power stroke of the bow is 57 cm; that is, the bowstring exerts force on the arrow through a displacement of 57 cm. The peak draw weight of the bow is 312 N. (This is the maximum force that the archer has to exert on the bowstring.)

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  1. 2 May, 16:13
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    156.24N

    Explanation:

    From the data above;

    Mass = 23g = 0.023kg

    V = 88m/s

    Kinetic energy = ½mv²

    K. e = ½ * 0.023 * 88²

    K. E = 89.056J

    The force required to accelerate the arrow to that speed and energy in 0.57m

    Using equation of motion;

    V² = U² + 2as

    But U = 0

    V² = 2as

    a = v²/2s

    a = 88² / (2*0.57)

    a = 6792.98m/s²

    The force (F) that accelerates the arrow with that velocity = ?

    F = M*a

    F = 0.023 * 6792.98

    F = 156.24N
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