A box with an initial speed of #7 m/s# is moving up a ramp. The ramp has a kinetic friction coefficient of #2/7 # and an incline of #( 5 pi )/12 #. How far along the ramp will the box go?
1 Answer
Explanation:
We're asked to find the distance traveled by the box given its initial speed, coefficient of kinetic friction, and angle of inclination.
NOTE: the friction force actually acts down the incline as opposed to the image (because the box is traveling up the ramp).
The magnitude of the kinetic friction force
where

#mu_k# is the coefficient of kinetic friction (#2/7# ) 
#n# is the magnitude of the normal force exerted by the incline plane, equal to#mgcostheta#
We must first find the acceleration of the box, using Newton's second law:
The net horizontal force
Therefore, we have
Plugging in known values, we have
directed down the incline, so this can also be written as
Now, we can use the equation
to find the distance it travels up the ramp before it comes to a stop.
Here,

#v_x = 0# (instantaneously at rest at maximum height) 
#v_(0x) = 7# #"m/s"# (given initial velocity) 
#a_x = 10.2# #"m/s"^2# 
#Deltax = # trying to find
Plugging in known values, we have