A6.0-kg box slides down an inclined plane that makes an angle of 39° with the horizontal. if the coefficient of kinetic friction is 0.40, at what rate does the box accelerate down the slope?
a. 3.1 m/s2
b. 3.4 m/s2
c. 3.7 m/s2
d. 4.1 m/s2

a.

Explanation:

The equation of the forces along the directions parallel and perpendicular to the slope are:

- Along the parallel direction:

where :

m = 6.0 kg is the mass  of the box

g = 9.8 m/s^2 the acceleration of gravity

 is the angle of the slope

is the coefficient of friction

R is the normal reaction  

a is the acceleration

- Along the perpendicular direction:

From the 2nd equation, we get an expression for the reaction force:

And substituting into the 1st equation, we can find the acceleration:

Solving for a,

the answer for apex is the lowest