Sally is on a canoe that comes to a stop a small distance from the dock. Since it is such a small distance, Sally decides to jump to the dock. She makes the jump, but the canoe moves away from her as she jumps. Since Sally is interested to see what happens on other boats, she makes the same jump from a fishing boat that is much larger than the canoe. Which boat will move away from Sally more quickly?

a. The canoe will move away from Sally more quickly because the fishing boat is larger in mass.
b. The fishing boat will move away from Sally more quickly because it is larger in mass.
c. Both boats will move away at the same speed because Sally has not changed mass and momentum must be conserved.
d. It is impossible to predict which boat moves away from Sally more quickly.

For this exercise we must define a system consisting of the girl, Sally and the boat, in one case the canoe and in the other the fishing boat; for this system we can use moment conservation

Initial moment. Before the jump

p₀ = (M + m₂) v

Final moment. After the jump

[tex]p_{f}[/tex] = M v₁ - m₂ v₂

Where m and v are the masses and speed of the canoe

p₀ = p_{f}

(M + m₂) v = M v₁ - m₂ v₂

In the case of changing the canoe for the heaviest fishing boat, the final moment is

p_{f} = M v₁ - m₃ v₃

p₀ = p_{f}

(M + m₃) v = M v₁ - m₃ v₃

Since the canoe is stopped the speed v = 0, we write the speed of each boat

Canoe

0 = M v₁ - m₂ v₂

v₂ = M / m₂ v₁

Fishing boat

0 = M v₁ - m₃ v₃

v₃ = M / m₃ v₁

Since the masses of the fishing boat (m₃) is greater than the mass of the canoe (m₂) the speed of the fishing boat is less than the speed of the canoe, we can find the relationship between the two speeds

v₂ / v₃ = m₃ / m₂

Here you can see what v₂> v₃ velocity canoe is more than velocity fishing boat