Finding speed at half the height given initial velocity and mass

[rockchalk1312]

In the figure, a frictionless roller coaster car of mass m = 800 kg tops the first hill with speed v0 = 18 m/s at height h = 44 m. What is the speed of the car at point B?

(point B is one half the height of the top of the first hill)


(1/2)mv²
W_g=mgd


(1/2)(800)(18²)=129600
129600/2=64800=(1/2)(800)(v²)
v=12.7m/s

This was wrong. Is the kinetic energy not just cut in half when height is halved? Thank you!

 

[berkeman]

In the figure, a frictionless roller coaster car of mass m = 800 kg tops the first hill with speed v0 = 18 m/s at height h = 44 m. What is the speed of the car at point B?

(point B is one half the height of the top of the first hill)


(1/2)mv²
W_g=mgd


(1/2)(800)(18²)=129600
129600/2=64800=(1/2)(800)(v²)
v=12.7m/s

This was wrong. Is the kinetic energy not just cut in half when height is halved? Thank you!

It's hard to decipher what you are doing. You know the total energy TE is the sum of the PE and KE, and it is constant at all times because of the frictionless track. Write the explicit sum for each of the points on the track...