A 8.5 dog takes a nap in a canoe and wakes up to find the canoe has drifted out onto the lake but now is stationary. He walks along the length of the canoe at 0.47 , relative to the water, and the canoe simultaneously moves in the opposite direction at 0.17 .What is the mass of the canoe?
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690
A 9.1 kg dog takes a nap in a canoe and wakes up to find the canoe has drifted out onto the lake but now is stationary. He walks along the length of the canoe at 0.48 m/s , relative to the water, and the canoe simultaneously moves in the opposite direction at 0.14 m/s .
To answer this question, we can use the conservation of momentum principle.
The momentum of an object is defined as the product of its mass and velocity. According to the conservation of momentum principle, the total momentum before an event should be equal to the total momentum after the event, assuming no external forces act on the system.
Let's denote the mass of the dog as Md, the velocity of the dog relative to the water as Vd, the mass of the canoe as Mc, and the velocity of the canoe relative to the water as Vc.
Given information:
- Vd = 0.47 m/s (velocity of the dog)
- Vc = -0.17 m/s (negative value because it is in the opposite direction)
- Md = 8.5 kg (mass of the dog)
We can now set up the conservation of momentum equation:
(Md * Vd) + (Mc * Vc) = 0
Substituting the given values, we get:
(8.5 kg * 0.47 m/s) + (Mc * -0.17 m/s) = 0
Simplifying the equation:
4.0 kg*m/s - 0.17 Mc kg*m/s = 0
Adding 0.17 Mc kg*m/s to both sides:
4.0 kg*m/s = 0.17 Mc kg*m/s
Dividing both sides by 0.17 kg*m/s:
Mc = 4.0 kg*m/s / 0.17 kg*m/s
Mc ≈ 23.53 kg
Therefore, the approximate mass of the canoe is 23.53 kg.