Block slides down a slope question (force and time)

[physicsguy112]

Homework Statement

A small block slides down a slanted board when released. The upper half of the board is smooth and the lower is rough, so that the acceleration of the block on the smooth half is three times greater than it is on the rough half. The block reaches the bottom of the board in time t1. The board is then flipped so that the upper half is rough and the lower part is smooth, and the block is released from the top again. This time, the block reaches the bottom of the board in time t2. In both cases, the board makes the same angle with the horizontal. Find the ratio t1/t2.

Homework Equations

Vf=Vo+at

F=ma

The Attempt at a Solution

I think I'm going to have to solve it in 2 parts, solve for t1 and t2 separately. When solving for t1 or t2, do I need to split up the rough and smooth surfaces?

I'm having trouble getting this one setup. I would really appreciate a strategy to help me solve this one. Thanks in advance for the help.

 

[member 553083]

For t1:We can set up the equations for the two parts of the board. For the smooth half: Vf = Vo + at 0 = Vo + 3at Vo = -3at For the rough half: Vf = Vo + at Vf = -3at + at Vf = -2at Now, we can combine the equations to get: 0=-3at -2at -5at = 0 at = 0 So, the time it takes for the block to reach the bottom of the board is: t1 = Vo/a = 0/0 = undefined For t2: We can set up the equations for the two parts of the board. For the rough half: Vf = Vo + at 0 = Vo + at Vo = -at For the smooth half: Vf = Vo + at Vf = -at + 3at Vf = 2at Now, we can combine the equations to get: 0=-at -2at -3at = 0 at = 0 So, the time it takes for the block to reach the bottom of the board is: t2 = Vo/a = 0/0 = undefined Therefore, the ratio of t1/t2 is undefined.