two 70 kg skiers, A and B, race on a pair trails down a mountain. Both trails dr

Question

two 70 kg skiers, A and B, race on a pair trails down a mountain. Both trails drop a vertical distance of 120m. Skier A chooses a trail that zigzags back and forth and has a total length of 1200m. Skier B chooses a trail that heads straight down the steepest part of the mountain and has a total length of 300m. ignore friction and air resistance. a) which skier is moving faster at the bottom of the mountain ? b) which skier will get to the bottom first ? c) the skier is hauled back to the top of the mountain by a tow rope. it operates at a speed 1.5 m/s up a frictionless tow track of lenght 450 m, up to a height of 120m. what is the average power required to lift skier A?

show work please

Explanation / Answer

mass of the skiers, mA=mB=70 kg

vertical distance, h=120 m

total length of the skier A is lA=1200m

total length of the skier B is lB=300m

a)

at the bottem of the end,

skier A moves faster than the skier B

b)

at the bottem of the end,

skier B will get the bottom first

c)

height, h=120 m

track length, l=450 m

speed, v=1.5 m/sec

tike taken, t=l/v

=450/(1.5)

=300 sec

now,

power P=m*g*h/t

=(70*9.8*120)/300

=274.4 W

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