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## Homework Statement

Starting from rest an 11kg block slides 11.9m down a frictionless ramp (inclined at 30° from the floor) to the bottom. The block then slides an additional 26.3m along the floor before coming to a stop. The acceleration of gravity is 9.8 m/s^2. Find the speed of the block at the bottom of the ramp.

## Homework Equations

Vf^2=vi^2+2a(d-do)

Conservation of energy: Ebefore=Eafter

KE=.5mv^2

PE=mgh

## The Attempt at a Solution

I tried solving this two differant ways, and both gave me the same answer, which was wrong. First I tried kinematics.

Vf^2=vi^2+2a(d-do)

Vf=sqrt(2*9.8/sin30*11.9)

(I used 9.8/sin30 because 9.8 is the vertical component, so 9.8/sin30 is the acceleration down the ramp)

Vf=21.598

The other way I tried used conservation of energy.

h=11.9/sin30=23.8

PE=KE

mgh=.5mv^2

gh=.5v^2

v=sqrt(9.8*23.8/.5)

v=21.598

I don't see where I went wrong in my logic, so I would greatly appreciate some guidance. Thank you!

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