Conservation of Momentum of a skydiver

[James98765]

I reading a physics book on my own right now and I appear to be stuck. The problem is as follows:

A 10 m long glider with a mass of 680 kg (including the passengers) is gliding horizontally through the air at 30 m/s when a 60 kg skydiver drops out by realesing his grip on the glider. What is the glider's velocity just after the skydiver let's go?

The problem is dealing with the law of conservation of momentum. I feel like I understand the concept except this particular problem is confusing me. I have defined the system as glider + skydiver. The problem is that gravity is an external force acting on the system so momentum shouldn't be conserved. I don't quite know how to handle this. If anyone could help me that would be great. Thanks a lot!

-James

 

[Doc Al]

Forget about gravity. Just worry about the "moment" when the skydiver drops. Hint: How does the momentum of the skydiver change when he let's go?

 

[James98765]

That's a good suggestion but I still don't understand one thing. Inorder for there to be a change in momentum their must be an impulse. Because the glider is supposed to gain vertical momentum, wouldn't there have to be a vertical impulse acting on the glider. I don't see how the skydiver letting go could cause I vertical impulse.

 

[Doc Al]

Why do you think the glider is supposed to gain vertical momentum?

 

[James98765]

It seems to make sense. If the skydiver is gaining downward vertical momentum shouldn't the glider have to gain upward vertical momentum due to the law of conservation of momentum. I guess that the momentum increase of the skydiver in the down direction is due to an external force (gravity). So that would mean that the glider wouldn't neccessarily have to accelerate upward. Does the glider change momentum in the horizontal direction? If so, where is the impulse in the horizontal direction causing the change?

 

[Doc Al]

It seems to make sense. If the skydiver is gaining downward vertical momentum shouldn't the glider have to gain upward vertical momentum due to the law of conservation of momentum. I guess that the momentum increase of the skydiver in the down direction is due to an external force (gravity). So that would mean that the glider wouldn't neccessarily have to accelerate upward.

Exactly.

Does the glider change momentum in the horizontal direction? If so, where is the impulse in the horizontal direction causing the change?

What makes you think there's a change in horizontal momentum?

 

[James98765]

I think I am coming to the conclusion that the glider doesn't change velocity at all because there is no impulse acting on it. I can't check my answer because it isn't in the book but the conclusion seems valid.

 

[Doc Al]

I think I am coming to the conclusion that the glider doesn't change velocity at all because there is no impulse acting on it.

You are correct. Neither glider nor skydiver change velocity at the instant he let's go.

 

[James98765]

Okay thanks a lot for your help! I think I fell for a trick question from my textbook. I wasn't expecting that. Thanks again! You lead me to a conclusion perfectly!

-James