A 0.066 kg arrow is fired horizontally. The bowstring exerts an average force of 75 N on the arrow over a dist

Question

A 0.066 kg arrow is fired horizontally. The bowstring exerts an average force of 75 N on the arrow over a distance of 0.85 m. With what speed does the arrow leave the bow?

Answer 1

This problem is about kinetic energy, work, and conservation of energy.

KE=1/2mv^2, where KE is the kinetic energy in J, m the mass in kg, and v the velocity in m/s. Substitute known values:

KE=1/2*0.066*v^2
=0.033v^2


Work = f*s, where f is the force in N and s is the displacement in meters. Substitute known values:

Work=75*0.85
=63.75

Based on the principle of conservation of energy,
KE=Work

.033v^2=63.75
v^2=63.75/0.033
=1931.8
v=43.95m/s