Does Distance Affect the Outcome in the Monkey and Zookeeper Problem?

[kghosh]

This may be a stupid question. In Hewitt physics book there is a problem where a zookeeper on the ground is trying to shoot a monkey on top of a tree. If the monkey drops at the same time as the zookeeper shoots, where should the zookeeper aim, above the monkey, at the monkey or below the monkey? The answer is "at the monkey" because the bullet will fall through the same amount as the monkey in the same amount of time.

My question is does the distance between the zookeeper and the tree where the monkey is have no effect at all?

 

[256bits]

Look at it this way, it might be easier to visualize.

The zookeeper is on a cliff, at the same height as the monkey on the tree - ie the zookeeper and monkey are at the same level.
The zookeeper shoots and the monkey drops at the same time.
The bullet and monket fall the same distance in the same anount of time.

If the cliff and monkey in a tree ares farther apart from each other, the distance fallen will increase, but the bullet will still hit the monkey.

With no air resistance the time for a hit is the time it takes the bullet to travel the distance of the cliff to the tree.

With air resistance the time will increase ( the bullet is slowing down in the horizontal direction )( neglect vertical air resistance for the monkey and bullet ) . The cliff and tree would have to be somewhat higher up from the ground.

 

[berkeman]

This may be a stupid question. In Hewitt physics book there is a problem where a zookeeper on the ground is trying to shoot a monkey on top of a tree. If the monkey drops at the same time as the zookeeper shoots, where should the zookeeper aim, above the monkey, at the monkey or below the monkey? The answer is "at the monkey" because the bullet will fall through the same amount as the monkey in the same amount of time.

My question is does the distance between the zookeeper and the tree where the monkey is have no effect at all?

When the zookeeper is on the ground, at a lower level than the monkey, I do not believe aiming at the monkey is the right approach.

If the zookeeper is level with the monkey (on the cliff that 256 used in his example), then firing horizontally is correct since the bullet drops vertically at the same rate as the monkey.

But when the zookeeper is below the monkey, if he aimed up at the monkey, the bullet will have a positive vertical velocity at first, until it reaches the top of its parabolic arc. That means that the bullet is rising as the monkey is falling at first, which means that the bullet will pass above the falling monkey.

Are you sure you have stated the textbook problem correctly? Can you scan a copy of the problem and attach it here?

 

[atyy]

When the zookeeper is on the ground, at a lower level than the monkey, I do not believe aiming at the monkey is the right approach.

If the zookeeper is level with the monkey (on the cliff that 256 used in his example), then firing horizontally is correct since the bullet drops vertically at the same rate as the monkey.

But when the zookeeper is below the monkey, if he aimed up at the monkey, the bullet will have a positive vertical velocity at first, until it reaches the top of its parabolic arc. That means that the bullet is rising as the monkey is falling at first, which means that the bullet will pass above the falling monkey.

Are you sure you have stated the textbook problem correctly? Can you scan a copy of the problem and attach it here?

But how about ?

 

[berkeman]

In fact, if you write the two equations for the height of the bullet as a function of time, and the height of the monkey as a function of time, aiming at the monkey only works for one special case of tree height and distance to the tree (for a particular bullet velocity), I believe...

 

[berkeman]

But how about ?

Hmm. Weird. It looks like they are aiming below the initial monkey position, but they say they are aiming at it.

Wonder where my thinking is wrong.

Yb(t) = 0 + Vy(0) - 1/2 g t^2

Ym(t) = H - 1/2 g t^2

So for Yb(t) = Ym(t), you need Vb(0) in the vertical direction multiplied by the flight time to equal H. Guess I need to play with this some more...

 

[berkeman]

Hah, I'll be danged!

H = Vy(0) * t = Vy(0) * L/Vx(0) = L * Vy(0)/Vx(0) = L * tan(theta) = H

Poor monkey!


EDIT: Fixed sin --> tan in equation above and in quote of it below.

 

[atyy]

Hah, I'll be danged!

H = Vy(0) * t = Vy(0) * L/Vx(0) = L * Vy(0)/Vx(0) = L * tan(theta) = H

Poor monkey!

https://www.physicsforums.com/showpost.php?p=2573188&postcount=4!

 

[berkeman]

https://www.physicsforums.com/showpost.php?p=2573188&postcount=4!

Geeze, in General Relativity no less. Physics Monkey looks worried...

Well, the bullet is certainly going to hit the monkey, because they will both impact on the singularity.

 

[kghosh]

Thanks for all the answers. I get that the shot has to come from the same height (found a similar problem in Giancoli and that one states specifically the shot is coming from the same level).

But I am still a little perplexed (even after seeing the MIT demonstration) and I still have a question.

The range a projectile will travel depends on the initial horizontal velocity. So, to me it looks like if the horizontal velocity is too small (or the distance between the tree and the zookeeper is too great) the bullet might fall to the ground before it covers the range. It will fall to the ground at the same rate as the monkey and at the same time as the monkey but the distance between the two will still matter.

Could you guys please clarify this? Thanks.

 

[berkeman]

Thanks for all the answers. I get that the shot has to come from the same height (found a similar problem in Giancoli and that one states specifically the shot is coming from the same level).

But I am still a little perplexed (even after seeing the MIT demonstration) and I still have a question.

The range a projectile will travel depends on the initial horizontal velocity. So, to me it looks like if the horizontal velocity is too small (or the distance between the tree and the zookeeper is too great) the bullet might fall to the ground before it covers the range. It will fall to the ground at the same rate as the monkey and at the same time as the monkey but the distance between the two will still matter.

Could you guys please clarify this? Thanks.

Yes, if the range is long enough that the bullet hits the ground short of the tree, the monkey will obviously not be hit by the bullet.