Projectile motion: aiming at a monkey

[kingwinner]

1) Suppose the zookeeper must shoot the banana from the banana cannon to the monkey who hangs from the limb of a tree. If the monkey lets go of the tree the moment that the banana is fired, then where should she aim the banana cannon?

 

The answer is to aim directly on the monkey, but I don't understand why!

I can only understand the special case when the cannon is at the same height as the monkey and is shot horizontally aiming at the monkey, they will drop by the same distance because horizontal and vertical components of a projectile motion are independent.

 

However, I don't understand the case above. Can somebody briefly explain the reason to me? Thanks a lot! :steering:

[Boerseun]

Quite easy, actually.

 

If you are quite a distance away from a target, and aim directly for it, your bullet will fall towards the earth in its ballistic trajectory. The further you are away, the higher you should aim to compensate for your bullet's drop.

 

But if you aim for the bull's eye, and the target falls of its mountings at the exact same time you pull the trigger, you'll hit it dead-on, because the target and your bullet falls towards the earth at the same rate.

 

Same with the monkey.

 

Although you should specify whether your monkey is shaved or not, seeing as a shaved monkey would be more airodynamic.

 

So tell me - did you shave your monkey?

[kingwinner]

Quite easy, actually.

 

If you are quite a distance away from a target, and aim directly for it, your bullet will fall towards the earth in its ballistic trajectory. The further you are away, the higher you should aim to compensate for your bullet's drop.

 

But if you aim for the bull's eye, and the target falls of its mountings at the exact same time you pull the trigger, you'll hit it dead-on, because the target and your bullet falls towards the earth at the same rate.

 

Same with the monkey.

 

Although you should specify whether your monkey is shaved or not, seeing as a shaved monkey would be more airodynamic.

 

So tell me - did you shave your monkey?

Well, we ignore air resistance for this case.......

 

"the target and your bullet falls towards the earth at the same rate"

I agree with that acceleration in the vertical direction is 9.8m/s^2[down], but the 2 objects are not dropping from the same height, and the bullet has initial vertical velocity while the monkey has no initial vertical velocity........then why would something like the animation above happen? I still don't get it......:steering:

[TheBigDog]

Well, we ignore air resistance for this case.......

 

"the target and your bullet falls towards the earth at the same rate"

I agree with that acceleration in the vertical direction is 9.8m/s^2[down], but the 2 objects are not dropping from the same height, and the bullet has initial vertical velocity while the monkey has no initial vertical velocity........then why would something like the animation above happen? I still don't get it......:steering:

When you throw a ball into the air it leaves your hand at speed X. From the moment it leaves your hand it begins accellerating toward the ground at 9.8m/s^2. But before it actually begins moving toward the earth it must first erode its upward velocity. So it doesn't matter if an object is moving up or down, the accelleration of gravity has the same relative effect.

 

That is why you aim straight at the monkey's mouth. If the monkey didn't let go the banana would be too low because of gravity pulling it toward the earth as it travels. But because the monkey starts to fall at the same moment that the banana, released from the cannon, begins to accellerate toward the earth they meet up perfectly.

 

Kingwinner, beside from a baby smooth monkey, what other variables could come into play in this experiment in the real world?

 

Bill

[Qfwfq]

but the 2 objects are not dropping from the same height, and the bullet has initial vertical velocity while the monkey has no initial vertical velocity

If you work it out right, you can see that the term with g in it is the same for both objects, since by definition the time is also the same for both, so it detracts the same height from both regardless of the differences you mention. The essential thing is that the monkey's path is vertical, so the difference between the banana's final position, with or without the g term, is also vertical, if you know what I mean.

 

This is a great example of a question designed to test how well a person thinks about such problems.

[cwes99_03]

Sorry Boer, Big D, Q has the best answer (mathematically speaking) but you all win an award for being quite right.

[Qfwfq]

Ya gotta recognize Boerseun's good remark about shaving the monkey! :confused:

[cwes99_03]

Yah, I really liked it. Always important to get a good laugh out of an honestly true answer.

[TheBigDog]

Kingwinner, beside from a baby smooth monkey, what other variables could come into play in this experiment in the real world?

No players?

 

Bill

[Boerseun]

No players?

 

Bill

'Course there are!

 

For starters, does the banana have a tailwind?

Is there an updraught?

Turbulence?

In-flight movie? :confused:

 

All these variables will have a profound influence on the outcome!

[InfiniteNow]

Is it a banana or a plantain?

 

Is it peeled or not?

 

Has the monkey had any daquaris?

[Qfwfq]

No it's a boomerang!

 

:confused:

[cwes99_03]

What I'm most interested in is the type of cannon. Is it a rail cannon that uses electromagnetic propulsion of the projectile? How ripe is the banana, and how old is the monkey? Which one smells worse?

[Qfwfq]

How ripe is the banana?

 

Bananas are best when straight off the plant, yellow and black. A friend of mine from Cotè d'Ivoire says you should be able to open them at the stem with the back of a limp finger.

[TheBigDog]

I guess Kingwinner isn't coming back to this one. Anyway, I was thinking along the lines of the shape of the banana. It probably has funky enough aerodynamic properties that it is not going to take a reliable path. And it is possible that it may even take on frisbee like properties that would make it a lifting body at high a speed and reduce the role of gravity in its descent.

 

Bill

[Qfwfq]

I was thinking along the lines of the shape of the banana.

I say, the boomerang!!!!!!

[TheBigDog]

I say, the boomerang!!!!!!

So if you miss the monkey you hit the cannon! Self reloading?