(adsbygoogle = window.adsbygoogle || []).push({}); [SOLVED] Conservation of Momentum and Thrown Objects

As part of our physics class, we've been given lots of problems typically solved by taking into account the law of conservation of momentum. I've had little-to-no trouble solving them, but one problem in particular is driving me nuts.

1. The problem statement, all variables and given/known data

There is a 50 kg girl in a 50 kg stationary canoe holding 2 10 kg cannon balls. She throws a cannon ball at 5 m/s, and then throws the second at 5 m/s w.r.t the boat. What is the canoe's final velocity if the (incorrect) assumption is made that their is no friction between the canoe and the water?Answer: 0.87 m/s

2. Relevant equations

[tex]

\vec{p} = \vec{p \prime}

[/tex]

3. The attempt at a solution

Ok, so I first calculate the speed of the canoe w.r.t the ground using the law.

[tex]

0 = \vec{p_c} + \vec{p_b}

[/tex]

[tex]

0 = 110 v_c + 10(5)

[/tex]

[tex]

v_c = -5/11 m/s \approx -0.454545454... {m/s}

[/tex]

Next, my idea was that the fact the second ball is being thrown at 5 m/s w.r.t. the canoewhile the canoe was movingwas important. So I used the L. of C. of M. again but in the frame of reference of the canoe.

[tex]

0 = 100v_c + 5(10)

[/tex]

[tex]

v_c = -1/2

[/tex]

So I figured I would just add the speed in the frame of reference of the boat to the speed it was traveling before. That gives me

[tex]

v_c \approx -0.95454545... m/s

[/tex]

Which is clearly not the right answer. Am I on the wrong track completely, or is there something simple I've missed? Any help would be appreciated. :)

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# Homework Help: Conservation of Momentum and Thrown Objects

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