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## Homework Statement

A block of wood slides first down and then up a ramp inclined at 25°. Assume the block/ramp kinetic friction coefficient = 0.2. The block starts from rest at position located 3.2 m up from the lowest point on the ramp. After sliding down, the block bounces back at the lowest point. The speed just after the bounce is only 87% of what it was just before the bounce.

a) Draw the free-body diagram for the block during the downward motion.

b) Using the above diagram, find the block's acceleration on the way down.

c) How much time does the block travel until it hits the lowest point?

d) Draw the free-body diagram for the block during the upward motion.

e) Using this diagra, find the block's acceleration on the way up.

f) Find the time the block spends moving up after the bounce until it reaches the highest point.

g) How far is that point from the bounce-point?

## Homework Equations

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## The Attempt at a Solution

a) I have the FBD drawn correctly, no help needed here.

b) a = -g sin(25°) - 0.2cos(25°)

a =

**-2.37 m/s^2**(

*I am pretty sure this is correct as well)*

c) time = square root of 2d/a = square root of (2(3.2)/2.37)

t =

**1.64 seconds**(

*not feeling good about this part*)

d) No help needed on the FBD.

e) -g sin(25°) + 0.2cos(25°)

a =

**-5.92 m/s^2**

f) velocity = t * |a| = 1.64 * 2.37 = 3.89 m/s

3.89 * 82% = 3.19 m/s

t = v/|a| = 3.19/5.92 =

**0.54 seconds**

g) distance = v*t

d = (3.19)(0.54) =

**1.72 m**

I don't feel like I did c, f, or g correctly. Sorry this was so long and probably hard to read. I am just getting used to this! Any help would be appreciated, even if it is only for one of the letters. Thank you!