Cons of Energy (assume no friction)?

Question

A 500kg roller coaster car is pulled to the top of a hill 45m high and arrives with a speed of 4m/s.



* How fast will the car go when at a point 29m above ground?

Answer 1

Total energy at the top of the hill is:

mgh + 1/2mv^2 = T where h = 45 meters, and v = 4 m/s

Total energy at 29 m height is

T2 = mgH +1/2mV^2 where H = 29 meteres and V is unknown.

Since energy is conserverd

T=T2 ---> mgh + 1/2mv^2 = mgH +1/2mV^2

Solve for V:

2g(h-H) + v^2 = V^2

V =sqrt(2g(h-H) + v^2) = 18.15 m/s