physics
posted by luc .
A box of books weighing 280 N is shoved across the floor of an apartment by a force of 390 N exerted downward at an angle of 35.1° below the horizontal. If the coefficient of kinetic friction between box and floor is 0.57, how long does it take to move the box 4.00 m, starting from rest?

Figuring the pushing force as horizontal and vertical forces is the first key. the horizontal component makes it move, the vertical force adds downward force increasing friction.
frictionforce=mu*forcenormal
= mu*(Weight+290sintheta)
Netforcemoving force=horizontalpushingfriction
= 290*cosThetamu(Weight290sinTheta)
but you know acceleration= netpushingforce/mass
so solve for a.
Then
distance=1/2 a*t^2 solve for t.