You are being pulled up a small slope by means of a rope tow

You are being pulled up a small slope by means of a rope tow. The angle of the slope is 14 degrees. Your mass including the board is 85 kg and the coefficient of kinetic friction between your board and the snow is 0.095. In order to pull you at a constant rate of 2 m/s. what is the tension in the rope? What will be your speed when you get to the top? What will be your acceleration when you head down the slope?

Solution

(a)
T - m*g*sin(14) - uk*m*g*cos(14) = m*a
As the rate is constant, acceleration = 0
T = m*g*sin(14) + uk*m*g*cos(14)
T = 85*9.8*sin(14) + 0.095 * 85 * 9.8 * cos(14)
T = 278.3 N

(b)
As the Pull is at constant rate, The velocity will be constant and equal to 2 m/s.
(c)
Acceleration when you head down the slope,
m*g*sin(14) - uk*m*g*cos(14) = m*a
9.8*sin(14) - 0.095*9.8*cos(14) = a
a = 1.47 m/s^2