Carmen and Judi dock a canoe. 83.0-kg Carmen moves forward at 4.3 m/s as she leaves the canoe to step onto the dock. At what speed and in what direction do the canoe and Judi move if their combined mass is 115 kg? (Use a positive number if the canoe moves away from Judi.)
Those are large girls. I am not so certain it is wise for Carmen to be walking in the canoe.
83*4.3=115*V
I don't understand the comment in the last ( ). Judi is in the canoe, the canoe cannot move away frm her.
To solve this problem, we need to understand and apply the principle of conservation of momentum. According to this principle, the total momentum before an event is equal to the total momentum after the event, assuming no external forces act on the system.
Let's denote the initial momentum of Carmen as "p1", the final momentum of Carmen after she steps onto the dock as "p2", the initial momentum of the canoe and Judi as "p3", and the final momentum of the canoe and Judi as "p4".
The law of conservation of momentum can be expressed as:
p1 + p3 = p2 + p4
We can obtain the values for p1, p2, and p3 from the given information.
Carmen's initial momentum (p1) is given by the product of her mass (m1) and her initial velocity (v1):
p1 = m1 * v1
Plugging in the values, we have:
p1 = (83.0 kg) * (4.3 m/s)
Next, Carmen's final momentum (p2) is equal to her mass (m1) multiplied by her final velocity (v2). Since Carmen steps onto the dock, her final velocity (v2) is 0 m/s:
p2 = m1 * v2
p2 = (83.0 kg) * (0 m/s)
The initial momentum of the canoe and Judi (p3) is given by the product of their combined mass (m3) and their initial velocity (v3). However, we need to determine the initial velocity of the canoe and Judi. Since the initial momentum is unknown, we'll call it "v3" for now.
p3 = m3 * v3
p3 = (115 kg) * (v3)
Finally, the final momentum of the canoe and Judi (p4) is given by their combined mass (m3) multiplied by their final velocity (v4):
p4 = m3 * v4
Now, let's rewrite the conservation of momentum equation using these values:
m1 * v1 + m3 * v3 = m1 * v2 + m3 * v4
Substituting the given values, we have:
(83.0 kg) * (4.3 m/s) + (115 kg) * v3 = (83.0 kg) * (0 m/s) + (115 kg) * v4
Now we can solve for v4, which is the velocity of the canoe and Judi after Carmen steps onto the dock.