Question

A 1.4 kg squash sits on top of a fence port. it is hit by an arrow moving with a speed of 1.8 m/s. just as they fall to the ground together the velocity is found to be 3 m/s. Find the mass of the arrow. (draw a picture of "before" and "after".)

Answer 1

Got to use conservation of momentum. Momentum = Mass x velocity

I am going to assume you have written the equation wrong, and that the arrow initial velocity is 3 m/s, and combined final velocity is 1.8 m/s. The way you have written the question, the arrow would have to have a negative mass of 3.5 kg, which is impossible as far as I know.

To solve the problem, we just write an equation that equates the 'before' and 'after' states of the system.

we will call the mass of the arrow 'm'

The initial momentum of the system is just going to be the mass of the arrow multiplied by the velocity of the arrow, as the squash is not moving, and therefore has a momentum = 0.

Initial momentum of the system = 3 m/s x (m)

Final momentum of the system = (1.4 kg + m) (1.8 m/s)

We then equate these two equations, and solve for the unknown value, m, which is the mass of the arrow.

3m = (1.4 + m)(1.8)

Solving for m, we get an arrow mass of 2.1 kg.