Monkey Bullet Proof: Analyzing Wrong Move

[MattWakes]

Homework Statement

A hunter on the ground aims his gun directly at a monkey hanging from a high tree branch some distance away. At the instant the gun is shot the monkey drops from the branch, hoping to avoid the bullet. Show analytically that the monkey made the wrong move. Ignore air resistance.

The Attempt at a Solution

I'm at something of a loss here. I think we're trying to show that the time for the monkey to drop is less than the speed of the bullet. So I tried to solve for t in terms of h and g for the bullet, because of the t: sqrt (2h/g) of the monkey, but got nowhere. There are no units here.. Any ideas?

 

[atyy]

Both the monkey and the bullet are acted on by gravity. Thus even though the hunter aims up at the monkey, his bullet will eventually fall. Is it possible that the bullet therefore hits the monkey?

 

[NascentOxygen]

Hi MattWakes! http://img96.imageshack.us/img96/5725/red5e5etimes5e5e45e5e25.gif

I'm at something of a loss here.

Me too! So it becomes a mind reading game...what was the lecturer likely thinking about when he set this question?

The gun is aimed "directly at the monkey" and it seems the monkey is some distance away. So I think we are to assume the hunter is failing to "aim high" to account for the bullet's path dipping due to gravity. (How was the monkey to know the hunter was such an amateur? He wasn't, so I don't really think we can accuse the monkey of misjudging his move.) It might carry more realism to say the hunter was using a bow and arrow, IMHO.

With this scenario, we have a clear picture to analyse. Is that better?

 

[SteamKing]

If there were units, how would that help you solve the problem?

 

[CWatters]

It appears the hunter has not aimed high to correct for the effect of gravity on the bullet. If the monkey hangs onto the branch the bullet might pass below him. If the monkey let's go he will fall into the path of the bullet. That's because the gun was pointed directly at him and both bullet and monket fall at same rate.

 

[vela]

Homework Statement

A hunter on the ground aims his gun directly at a monkey hanging from a high tree branch some distance away. At the instant the gun is shot the monkey drops from the branch, hoping to avoid the bullet. Show analytically that the monkey made the wrong move. Ignore air resistance.

The Attempt at a Solution

I'm at something of a loss here. I think we're trying to show that the time for the monkey to drop is less than the speed of the bullet. So I tried to solve for t in terms of h and g for the bullet, because of the t: sqrt (2h/g) of the monkey, but got nowhere. There are no units here.. Any ideas?

You can't compare a time with a speed. They're different types of physical quantities and have different units. It makes sense to say 20 m/s is bigger than 10 m/s, but saying 20 m/s is bigger or smaller than 1 hour doesn't.

The problem statement implies the monkey gets hit by the bullet and wants you to show this. How do you express mathematically the monkey getting hit by the bullet? In other words, what quantities have to be equal when the bullet hits the monkey?

 

[MattWakes]

Thanks so much for the responses. They went a long way in demystifying this question. I now know that if the gun is pointed directly at the monkey, the force of gravity will act on both identically so that the bullet (I agree, should be arrow) and monkey will meet in midair. The quantities that must be equal for this to occur are height and time, right? By manipulating a constant acceleration equation, I get that the height for the monkey is h=gt^2/2. For the bullet, I'm having trouble writing that in the same units because of velocity; h=vit-gt^2/2. Does velocity matter? If the gun was fired at 1m/s, it wouldn't have a prayer of hitting the monkey.

What am I missing?

The help is greatly appreciated.

 

[haruspex]

the height for the monkey is h=gt^2/2. For the bullet, I'm having trouble writing that in the same units because of velocity; h=vit-gt^2/2.

Define those heights - where are they measured from?

 

[MattWakes]

The height for the monkey would be hm=h-.5gt^2
For the bullet, hb=vit-.5gt^2. I assume they're measured from the top of the tree branch?
If the heights were the same, the question would be proven. However, how do I convert vit to height?

 

[haruspex]

The height for the monkey would be hm=h-.5gt^2
For the bullet, hb=vit-.5gt^2. I assume they're measured from the top of the tree branch?
If the heights were the same, the question would be proven. However, how do I convert vit to height?

Based on where the bullet was aimed, what would its height have been at that time t if there were no gravity?

 

[MattWakes]

Height h, the top of the branch, I expect. Then, vit converts to h and our quantities are equal. Yet how can I prove that mathematically?

 

[haruspex]

Height h, the top of the branch, I expect. Then, vit converts to h and our quantities are equal. Yet how can I prove that mathematically?

Which bit do you think is in need of more rigour?

 

[MattWakes]

Hey, I figured it out. Using trig, tan(theta)=vy/vx=dy/dx. Dy=vydx/vx.
Vit, if I substitute for t, is vydx/vx. Therefore, h of bullet= h-1/2gt^2, just as the height of the monkey. Thx for the help