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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?

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    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=horizontalpushing-friction
    = 290*cosTheta-mu(Weight-290sinTheta)
    but you know acceleration= netpushingforce/mass

    so solve for a.

    Then
    distance=1/2 a*t^2 solve for t.

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