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?

The speed of the arrow as it leaves the bow is 43.04 m/sec.

Given :

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

Average force, F = 105 N

Distance covered, s = 75 cm = 0.75 m

Initial speed of arrow, u = 0

Solution :

We know that,

Work Done = Final Kinetic Energy - Initial Kinetic Energy

here, Initial Kinetic Energy = 0 because initial velocity is zero. Therefore

 ---- (1)

where, v is final velocity, m is mass and W is work done.

We also know that,

Work Done = Force x Displacement

---- (2)

From equation (1) and (2) we get,

  ----- (3)

Now put the values of F, s and m in equation (3) we get,

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

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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

v = 43.04 m/s

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