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Question

An 85 g arrow is fired from a bow whose string exerts an average force of 10⁵ N on the arrow over a distance of 75cm. What is the speed of the arrow as it leaves the bow?

Answer 1

I think you value of applied force is incorrect, thus let use N=10^-5 N

Kinetic Energy and the Work-Energy Principle statement is net work = change of kinetic energy, Wnet=∆KE.

Now, work done on the arrow is W=Fd=(0.75 m)(10^-5 N)=7.5*10⁴ J

That amount of energy will convert into change of kinetic energy, that is, mV²/2=7.5*10⁴ J ( as initial V and KE was zero).

Now, you can calculate V=[(2*7.5*10^-4 J)/(0.085 kg)]^1/2=0.133 m/s