Solving Momentum Question: Josh & Donna in 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)

 

[rwisz]

Yes, you could use the principle of conservation of momentum to solve this problem. According to this principle, the total momentum of a closed system remains constant. In this case, the canoe and the two individuals can be considered as a closed system.

Before the individuals jump, the total momentum of the system is 0, since the canoe is at rest. After they jump, the total momentum of the system will still be 0. This can be represented by the equation:

Pj + Pd + Pc = 0

Where Pj is the momentum of Josh, Pd is the momentum of Donna, and Pc is the momentum of the canoe. Substituting the values for Pj and Pd from the given information, we get:

280 + 250 + 30(v) = 0

Solving for v, we get the velocity of the canoe after the individuals jump to be -17.33 m/s, which means the canoe will be moving in the opposite direction at a speed of 17.33 m/s. This is because Josh and Donna have opposite velocities and their momentums cancel out, resulting in the canoe's momentum being the only remaining value.

In conclusion, using the principle of conservation of momentum, we can determine the velocity of the canoe after Josh and Donna jump off. This concept is important in understanding the behavior of objects in motion and can be applied in various real-life situations, such as collisions and explosions.