After shooting a 28g arrow with an initial velocity of 92m/s[forward], an archer standing on a frictionless surface travels in the opposite direction at a speed of 0.039m/s. Calculate the combined mass of the archer and the bow.
Given: **Subscript of 1 indicates values for the arrow and subscript of 2 indicates values for the archer
The Attempt at a Solution
The only way this problem works is if you treat the archer and the bow as one body/one object and using the above formula and values, solve for m2:
I got the correct answer aside from the negative sign in front of my answer. Why is my answer negative? Does that mean I did something wrong?
Also, why do you treat the archer and the bow as one collective object? I thought the law of conservation of momentum, which gives us the equation I used, applied to situations when two objects collide in an isolated system. If so, then what collision occurs in this problem; how are both the bow and the archer colliding with the arrow?