An 80 kg person decides to jump off the back end of a 30 kg canoe. His friend measures the speed of the canoe after he jumps to be 0.8 m/s. The canoe was initially at rest. What rule would I use to find the speed of the person who jumped?
initially there was 0 momentum. That momentum is conserved. So, assigning the canoe's direction as negative,
30*(-.8) + 80*v = 0
80v = 24
v = +.3m/s
conservation of momentum
initial mometum= final momentum
(80+30)Vc=30*.8-80*V
but Vc=0, the canoe was not moving initially. Solve for V
To find the speed of the person who jumped off the canoe, you can use the principle of conservation of momentum. According to this principle, the total momentum before the jump will be equal to the total momentum after the jump if no external forces are acting on the system.
The principle of conservation of momentum can be stated as follows: the total momentum of a system before any external forces act on it is equal to the total momentum of the system after the external forces have acted on it.
In this case, the initial momentum of the system (which includes the person and the canoe) is zero since the canoe is initially at rest.
The momentum of an object is defined as the product of its mass and velocity, so we can calculate the initial momentum by multiplying the mass of the person and canoe together with their initial velocity (which is zero):
Initial momentum = (mass of the person + mass of the canoe) × Initial velocity
= (80 kg + 30 kg) × 0 m/s
= 0 kg·m/s
After the person jumps off the canoe, the canoe starts to move in the opposite direction with a velocity of 0.8 m/s. Let's call the velocity of the person after the jump "Vp" (unknown at this point).
The final momentum of the system is the sum of the momentum of the person and the momentum of the canoe after the jump. Using the same mass and velocity definition, we can write:
Final momentum = (mass of the person) × (final velocity of the person) + (mass of the canoe) × (final velocity of the canoe)
= 80 kg × Vp + 30 kg × (-0.8 m/s)
= 80 kg × Vp - 24 kg·m/s
According to the principle of conservation of momentum, the initial momentum of the system is equal to the final momentum of the system. Therefore, we can set the initial momentum equal to the final momentum and solve for Vp:
0 kg·m/s = 80 kg × Vp - 24 kg·m/s
Rearranging this equation, we find:
80 kg × Vp = 24 kg·m/s
Simplifying further:
Vp = 24 kg·m/s / 80 kg
Vp = 0.3 m/s
So, the speed of the person who jumped off the canoe is 0.3 m/s.