- #1

Jessehk

- 21

- 0

**[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.

## Homework Statement

*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**

## Homework Equations

[tex]

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

[/tex]

## 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 canoe

*while the canoe was moving*was 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. :)