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 75 cm. what is the speed of the arrow as it leaves the bow?

Answer 1

Answer:

Speed of the arrow, v = 43.04 m/s

Explanation:

It is given that,

Mass of an arrow, m = 85 g = 0.085 kg

Average force exerted by the string of a bow, F = 105 N

Distance covered, d = 75 cm = 0.75 m

Initial speed of then arrow, u = 0

To find,

The speed of the arrow as it leaves the bow.

Solution,

Let u and v is the initial and the final speed of the arrow. We need to find the the speed of the arrow as it leaves the bow. Using work energy theorem to find it as :

Work done = Final kinetic energy - initial kinetic energy

$F.d=\dfrac{1}{2}mv^2$

$v=\sqrt{\dfrac{2Fd}{m}}$

$v=\sqrt{\dfrac{2\times 105\times 0.75}{0.085}}$

v = 43.04 m/s

Therefore, the speed of the arrow as it leaves the bow is 43.04 m/s.

Answer 2

Answer:

43 m/s

Explanation:

m = 85 g = 0.085 kg, F = 105 n, s = 75 cm = 0.75 m,

Let the speed is v.

According to work energy theorem

Change in kinetic energy = Work done

Final kinetic energy - initial kinetic energy = Work

1/2 x m x v^2 - 0 = F x s

0.5 x 0.085 x v^2 = 105 x 0.75

0.0425 v^2 = 78.75

v = 43 m/s