A 27g arrow is shot horizontally. The bowstring exerts an average force of 75N on the arrow over a distance of 78 cm. Determine, using the work...

The arrow that is being shot has a mass of 27 g. The bow
string exerts a force of 75N over a distance of 78 cm. The work done by the bow string
is stored in the arrow as kinetic energy. The kinetic energy that the arrow attains when
it leaves the bow is equal to (1/2)*m*v^2, where v is the maximum
velocity.

The work done on the arrow by the bow string is
given by force*displacement as the force acts in the same direction as the displacement
of the arrow. Here cos theta = cos 0 = 1.

Work done =
75*78/100 = 58.5 J

The kinetic energy (1/2)*m*v^2 =
58.5

=> (1/2)*(27/1000)*v^2 =
58.5

=> v^2 =
58.5*2000/27

=> v^2 =
13000/3

=> v = 65.85
m/s

The arrow has the maximum velocity when
it leaves the bow and it is equal to 65.85 m/s.