Momentum conservation when Josh and Donna jump from a canoe

[runningirl]

Homework Statement

A young man, Josh (m=70 kg) and his sister Donna (m=50 kg) are out on a canoe (m=30 kg). They begin to fight and she abruptly jumps off the end of the canoe at a speed of 5 m/s. Josh, immediately reacts by jumping off the opposite side of the canoe at 4 m/s. What is the velocity of the canoe after they both jump the lake?

Homework Equations

J=Fave(time)
P=(m)(v)

The Attempt at a Solution

Pj=70(4)=280
Pd=(50)(5)=250

Pc=30(v)

could i do Pj+Pd and then set it equal to Pc?!

 

[JesseC]

Well the initial momentum of the canoe plus the people before they jump off is zero. Therefore the final momentum of the canoe plus people is also going to be zero as momentum is conserved. So:

$$p_{Josh}+p_{Donna}+p_{canoe} = 0$$

Now you just need to think about the directions that Donna and Josh are travelling? You'll need to put a minus sign depending on the direction of their velocity.

 

[runningirl]

donna and josh would both have negative velocities because they're jumping off. (direction of their velocity).

 

[JesseC]

But if they both had negative velocity they'd both be traveling in the same direction right? The question says Josh and Donna jump off opposite ends of the canoe. So they can't be traveling in the same direction.

You're free to choose which direction is positive and which is negative, it won't make a difference to the final speed of the canoe. (Be careful of the difference between speed and velocity)