You have been hired by the college zoology department for the summer. You are ex

Question

You have been hired by the college zoology department for the summer. You are excited because you will be working with a world-famous expert on animal behavior. She has assigned you to study several videotapes of African animals leaping into the air from the ground. Your task is to compare the power output of several animals when they jump. You will be able to determine the mass of each animal from data on the animals collected in the field. By viewing the videotape, you will be able to measure both the vertical distance d over which the animal accelerates when it pushes off the ground and the maximum height h it reaches.

Explanation / Answer

First off let's look at the basic deffinition for power
P=w/t
we can replace w with mgh because that potential energy is equivelent to the energy put into work.
p=mgh/t
now t is a little harder to figure out, but it's not that complicated.

Because we know that the animals initial verticle velocity will be zero we can relate it's height to it's kinetic energy giving us an instantaneous speed from when the animal is at the height d(when the legs just leaving the ground)From conservation of energy we get

mgh=(1/2)mv2+mgd

v=(2(gh-gd))

from here we can look at the deffinition of acceleration

a=vf/t                                   (vf is the speed we found in the last step)

t=(2g(h-d))/a

where a is found with the equation

df=di+vit+(1/2)at2

a=2d/t2

plug it in

t=t2((2g(h-d))/2d)

t=2d/(2g(h-d))

So power can be written as

p=w/t

=mgh(2g(h-d))/2d

By the way if this were really being done it would be a whole lot easier to use the tapes to find the amount of time before the animal stops accerlerating.  This way insteat of a complicated function we end up with simply mgh/t

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