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## Homework Statement

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

m

_{1}=0.028kg

v

_{i1}=92m/s[forward]

v

_{f1}=0m/s

v

_{i1}=0.039m/s[backward]

vf

_{2}=0m/s

## Homework Equations

m

_{1}v

_{i1}+m

_{2}v

_{i2}=m

_{1}v

_{f1}+m

_{2}v

_{f2}

## 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 m

_{2}:

(0.029)(92)+m

_{2}(0.039)=0

2.576=-m

_{2}(0.039)

-66.05128205kg=m

_{2}

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?