Homework Help: Kinetic energy with ariplanes

1. Feb 2, 2008

rearview

1. The problem statement, all variables and given/known data
Which has a higher kinetic energy?
An airplane traveling at the speed of sound or an airplane with half the weight of plane one and traveling at 2 times the speed of sound?

2. Relevant equations
KE = 1/2 mv^2
v=gt

3. The attempt at a solution
I think I am just get mixed up on words. If they were the same weight the plane going twice as fast would have 4 times the kinetic energy. (v=2^2=4).
I think I am going the wrong direction. Would their kinetic energy be the same? Since plane two weight is half but double the speed. Help

2. Feb 2, 2008

AFG34

E1 = (1/2)(m)(v^2)

E2 =(1/2)(0.5m)(2v^2)
E2 =(.5)(2^2)(1/2*m*v^2)
E2 =(.5)(2^2)(E1)
E2 = 2E1

I think you multiplied the final 2 by the half that is in the equation for kinetic energy.

3. Feb 2, 2008

awvvu

Since the kinetic energy depends on the speed _squared_, doubling the speed will have more effect than doubling the mass. Try calculating both KE's.

4. Feb 2, 2008

rearview

I think I have it. Plane two will have the higher KE since KE is quadrupled with increase in speed. The weight is a factor but not as much as speed. Thanks