A question about conservation of momentum

[papercace]

Let's say you've got a boat filled with n frogs of mass m each. Let's also say that all the frogs jump simultaneously out of the boat in the same direction with velocity v, then the boat will get a velocity v₁ in the opposite direction because of conservation of momentum.

Now if we instead let each frog jump separately with velocity v, the boat will get a velocity v₂ that is bigger than v₁.

I did see the formula and the derivation for why the boat gets a different velocity, but I'm still not getting it intuitively. If the same mass is leaving the boat at the same velocity, why does the boats velocity differ depending upon when the mass leaves the boat?

 

[Buzz Bloom]

Hi papercace:

Perhaps the following will be helpful.

https://en.wikipedia.org/wiki/Impulse_(physics)​

Regard,
Buzz

 

[PeroK]

Let's say you've got a boat filled with n frogs of mass m each. Let's also say that all the frogs jump simultaneously out of the boat in the same direction with velocity v, then the boat will get a velocity v₁ in the opposite direction because of conservation of momentum.

Now if we instead let each frog jump separately with velocity v, the boat will get a velocity v₂ that is bigger than v₁.

I did see the formula and the derivation for why the boat gets a different velocity, but I'm still not getting it intuitively. If the same mass is leaving the boat at the same velocity, why does the boats velocity differ depending upon when the mass leaves the boat?

What happens if all the frogs do an identical jump (it terms of the mechanics of their jump)?

 

[A.T.]

If the same mass is leaving the boat at the same velocity, why does the boats velocity differ...

Those two velocities are relative to what?

 

[papercace]

Hi papercace:

Perhaps the following will be helpful.

https://en.wikipedia.org/wiki/Impulse_(physics)​

Regard,
Buzz

Yes I know what impulse is. If the frogs jump simultaneously, then the impulse time will be short but the force impacted on the boat will be large. If they jump one after the other, the force of each jump will be small but they will do it over a longer time. In the end they should add up to be the same impulse, I think.

What happens if all the frogs do an identical jump (it terms of the mechanics of their jump)?

Sorry I don't understand your question.

Those two velocities are relative to what?

Yeah I should have stated that. v is relative to the boat while v₁ and v₂ are relative to the water.

 

[Ibix]

Yeah I should have stated that. v is relative to the boat while v₁ and v₂ are relative to the water.

So what is the velocity of the frogs with respect to the water in the two cases?

 

[jbriggs444]

Yeah I should have stated that. v is relative to the boat while v1 and v2 are relative to the water.

That still leaves v ambiguous -- relative to the boat pre-leap, post-leap or mid-leap?