Question

An archer pulls a bowstring back a distance of 20 cm with an average force of 75 N. The arrow has a mass of 20.0 g. When he releases the string, what is the velocity of the arrow when it leaves the bow? (A) 1.2 m/s (B) 22 m/s (C) 32 m/s (D) 39 m/s (E) 42 m/s

Answer 1

To solve this problem we will apply the concepts related to the work theorem for which it is defined as the product of Force and distance. In turn, we will use the energy conservation theorem for which the applied work must be equivalent to the total kinetic energy on the body.

The work is defined as

$W = Fd$

Here,

F = Force

d = Displacement

Replacing with our values we have that

$W = 75*0.2$

$W = 15J$

Now by conservation of energy,

$W = KE$

$W = \frac{1}{2}mv^2$

$15 = \frac{1}{2} (20*10^{-3}kg)(v^2)$

Solving for v,

$v = 10\sqrt{15}$

$v = 38.72 \approx 39$

Therefore the correct answer is D.