A 79.7-g arrow is fired horizontally from rest. The bowstring exerts an average

Question

A 79.7-g arrow is fired horizontally from rest. The bowstring exerts an average force of 83.9 N on the arrow over a distance of 0.815 m. With what speed does the arrow leave the bow? A 79.7-g arrow is fired horizontally from rest. The bowstring exerts an average force of 83.9 N on the arrow over a distance of 0.815 m. With what speed does the arrow leave the bow? A 79.7-g arrow is fired horizontally from rest. The bowstring exerts an average force of 83.9 N on the arrow over a distance of 0.815 m. With what speed does the arrow leave the bow?

Explanation / Answer

Force, F = 83.9 N
Mass, m = 79.7 g = 0.0797 kg
Acceleration, a = F/m
= 83.9/0.0797
= 1052.698 m/s2.

Initial velocity, u = 0
Distance traveled, s = 0.815 m
Acceleration, a = 1052.698 m/s2.
Consider v as the final velocity.
Using the relation v2 - u2 = 2as
v2 - 0 = 2 x 1052.698 x 0.815
v2 = 1715.897
v = SQRT[1715.897]
= 41.42 m/s

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