Finding speed of roller coaster at different points

[joe426]

Homework Statement

Homework Equations

KE= 1/2 m v²
PE = mgy

The Attempt at a Solution

I'm not sure how to start this because there is no given mass. If I use a kinematics equation I don't have an acceleration.

 

[cbasst]

At point 1, the roller coaster only has potential energy (no kinetic energy because velocity is 0). At point 2, it will have lost all of its potential energy - the potential energy will have been converted into kinetic energy. Since no energy is being lost due to friction, PE₁ must be equal to K₂. Given that, can you figure the rest out? (Hint: set up the equation PE₁=K₂)

 

[joe426]

v = sqrt (2gy)
v = sqrt (2 * 9.8m/ss * 35m) = 26.19 m/s at point 2

But K₂ doesn't equal P₂ because K₂ equaled P₁ at a height of 35m, not 28m, right?

 

[cbasst]

But K2 doesn't equal P2 because K2 equaled P1 at a height of 35m, not 28m, right?

I don't know if I understand this question. Did you mean to say "But K2 doesn't equal P3 because K2..."? If you were asking about how to solve for velocity at P₃, do you think you could use a similar strategy that you did for point P₂? It may help if I point out that you are indirectly given the difference in height between P₁ and P₃.