# A box with an initial speed of 2 m/s is moving up a ramp. The ramp has a kinetic friction coefficient of 1/2  and an incline of (2 pi )/3 . How far along the ramp will the box go?

Jul 4, 2017

0.331m (3sf)

#### Explanation:

Resolving perpendicular to the slope:
R=mgcos$\left(\frac{2 \pi}{3}\right)$
R=$\frac{- m g}{2}$

F=$\mu$R

F=$\frac{- m g}{4}$

Resolving parallel to the slope:
0 - (F + mgsin$\left(\frac{2 \pi}{3}\right)$) = ma (mass cancels)

Using suvat:
s = $\frac{{v}^{2} - {u}^{2}}{2 a}$
s = 0.331m