Help on impossible physics problem?

Question

A T-bar tow is planned in a new ski area. At any one time, it will be required, to pull a maximum of 73 skiers up a 556-m slope inclined 15° at above the horizontal at a speed of 2.50 m/s. The coefficient of kinetic friction between the skiers skis and the snow is typically 0.055. As the manager of the facility, what motor power should you request of the construction contractor if the mass of the average skier is 74.0 kg. Assume you want to be ready for any emergency and will order a motor whose power rating is 50 percent larger than the bare minimum.

_____ kW

Answer 1

P = m*g*Vv + µ*m*g*Vcos15° = (73*74)*9.8*2.5sin15° + .055*(73*74)*9.8*2.5*cos15° = 41285.6 W

Pm = 1.5P = 61.9 kW

Answer 2

Here, work is done in 2 areas

1.  against the friction of the ice, along the slope

2.  vertically upwards, against the total weight

1.  Total weight  =  73 x 74 x 9.81  =  52994N

    Component of this perpendicular to the slope  =   52994 x cos(15)  =  51188N

    Frictional force along the slope  =  51188 x 0.055  =  2815N

   Power required to overcome ice friction  =  force  x  velocity  =  2815  x  2.5  =  7038W

2.  Total weight  =  52994N

   Vertical component of velocity  =  2.5 x sin(15)  =  0.647m/sec.

   Power required against gravity  =  force  x  velocity  =  52994  x  0.647  =  34287W

3.   Total power  =  34287  +  7038   =   41325W

    Increase by 50%   =   41325 x 1.5  =  61988W

    Say  = 62000W   =   62KW