Does a car's momentum change affect Earth's momentum equally?

[Tim Wu]

I find this problem kind of tricky. I think it must be a, since a change in momentum of the car causes the same change in momentum of the earth.

 

[Doc Al]

a change in momentum of the car causes the same change in momentum of the earth

That part is correct. But does that imply that the kinetic energy is the same? Compare the formulas for momentum and kinetic energy.

 

[Tim Wu]

That part is correct. But does that imply that the kinetic energy is the same? Compare the formulas for momentum and kinetic energy.

Oh yeah! Ek=1/2*m*v^2, and v = p/m, therefore Ek= p^2/2m. Since p is the same for car and Earth but the Earth's mass is way bigger the kinetic energy gained by Earth wud be much lower! So would option c be right?

 

[Doc Al]

Oh yeah! Ek=1/2*m*v^2, and v = p/m, therefore Ek= p^2/2m. Since p is the same for car and Earth but the Earth's mass is way bigger the kinetic energy gained by Earth wud be much lower! So would option c be right?

You got it. Good thinking!