Question

An archer pulls back 0.75 m on a bow which has a stiffness of 200 N/m. The arrow weighs 50 g. What is the velocity of the arrow immediately after release?

A
48.9 m/s
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B
47.4 m/s
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C
50.0 m/s
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D
45.0 m/s
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Solution

The correct option is B 47.4 m/sThe bow can be treated as a type of spring. The potential energy of a spring is: (12)kx2, Therefore,the potential energy PE of the bow is: PE = (12)(200)0.752 = 56.25 J The kinetic energy of a particle is (12)mv2, The arrow can be treated as a particle since it is not rotating upon release. Therefore, the kinetic energy KE of the arrow is: KE = (12)(0.05)v2 If we assume energy is conserved, then PE = KE Solving for the velocity of the arrow v we get v = 47.4 m/s.

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