SciForums.com > Science > Physics & Math > Projectile motion: aiming at a monkey PDA View Full Version : Projectile motion: aiming at a monkey Post ReplyCreate New Thread kingwinner03-04-06, 10:55 AM1) 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? http://www.physicsclassroom.com/mmedia/vectors/mzf.gif 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! :) Giambattista03-04-06, 11:15 AMWhy would someone need to do such a thing in the first place? Put the banana on the ground, and let the monkey get it there. Getting the banana to the monkey: a common sense approach. DaleSpam03-04-06, 11:56 AMHi Kingwinner, Consider the situation w/o gravity. In that case it is obvious that you have to aim right at the monkey, right? In the w/o gravity case the bananna goes in a straight line and so the effect of gravity can be thought of as a deviation from that straight line. If you do the math to figure out how big that deviation is you will find that at any point in time it is exactly the same as the distance that the monkey has fallen. So by the time the bananna reaches the monkey it has deviated from the straight line by the same distance that the monkey has fallen and so it hits the monkey. One intersting thing is that the actual acceleration due to gravity is irrelevant, only the timing and the aim is important. It doesn't matter if the monkey is on earth, the moon, or jupiter. -Dale Tom203-04-06, 01:27 PMWhy would someone need to do such a thing in the first place? Put the banana on the ground, and let the monkey get it there. Getting the banana to the monkey: a common sense approach. :rolleyes: This problem has nothing to do with either monkeys or bananas. It is designed to emphasize the fact that bodies subject to uniform gravitational fields fall at the same rate. Your objection doesn't address the many variants of this problem anyway. When I learned this problem it was not a banana cannon but rather a hunter with a rifle. But I guess the idea of using physics to find the best way to blow a falling monkey's brains out doesn't go over as well these days. kingwinner: You can work this out mathematically. Let the banana cannon be at the origin of a coordinate system, and let the monkey's initial cooridnates be (x0,y0). The equations of motion for the banana and monkey are: Banana Let the initial speed of the banana be v0 and the launch angle be θ. xB(t)=v0cos(θ )t yB(t)=v0sin(θ )t-(1/2)gt2 Monkey xM(t)=x0 yM(t)=y0-(1/2)gt2 Set the x and y coordinates of both the monkey and the banana equal and solve for θ . You will find that the angle is independent of both t and v0, and that it must be such that tan(θ )=y0/x0. In other words, the cannon must be pointed right at the monkey. CANGAS03-04-06, 11:28 PMDale: It will matter to the precious little minkee whether it is in a habitable Earth environment or one of those other nasty places you want to put it. Your gravitational fall rate analysis sure sounds good to me. I wish you were in charge of MY bananas at feeding time. DaleSpam03-05-06, 05:17 PMI wish you were in charge of MY bananas at feeding time.I just know that there must be some great double entendre response about bananas and perhaps peaches. Alas, it completely escapes me right now. :( -Dale CANGAS03-06-06, 01:30 AMNo double meaning. I sincerely wish that my providence had always been taken care of thoughtfully and on schedule. Post ReplyCreate New Thread