Problem. You are skiing downhill in Lake Tahoe Ski Resort. You start from the height 500 m above the lake level and slide 500 m over the run that makes 30° angle with respect to horizontal. Initially your speed is zero. Lake level 30° We learned from the last quiz that if you neglect friction and air resistance, your speed at the end of the run will be as large as 220 mph! Now lets account for friction and air resistance in your downhill run: a) What will be your speed at the end of the run if you take into account air resistance but neglect friction? Assume the drag coefficient 0.6, the air density is 1.2 kg/m³, the typical mass of a human 80 kg and its cross- sectional area 0.5 m², and that the skier will reach its terminal velocity at the end of the run. Give the final answer in miles per hour. Acceleration of gravity is 9.8 m/s², and 1 mile = 1.609 km. b) What will be your speed at the end of the run if you now account for friction between your skis and the snow but neglect air resistance? Assume the kinetic friction coefficient 0.5. Give the answer in miles per hour. c) What will be your speed at the end of the run if you take both friction and air resistance into account? Assume the same data as above and that the skier will reach its terminal velocity at the end of the run. Give the answer in miles per hour.
Problem. You are skiing downhill in Lake Tahoe Ski Resort. You start from the height 500 m above the lake level and slide 500 m over the run that makes 30° angle with respect to horizontal. Initially your speed is zero. Lake level 30° We learned from the last quiz that if you neglect friction and air resistance, your speed at the end of the run will be as large as 220 mph! Now lets account for friction and air resistance in your downhill run: a) What will be your speed at the end of the run if you take into account air resistance but neglect friction? Assume the drag coefficient 0.6, the air density is 1.2 kg/m³, the typical mass of a human 80 kg and its cross- sectional area 0.5 m², and that the skier will reach its terminal velocity at the end of the run. Give the final answer in miles per hour. Acceleration of gravity is 9.8 m/s², and 1 mile = 1.609 km. b) What will be your speed at the end of the run if you now account for friction between your skis and the snow but neglect air resistance? Assume the kinetic friction coefficient 0.5. Give the answer in miles per hour. c) What will be your speed at the end of the run if you take both friction and air resistance into account? Assume the same data as above and that the skier will reach its terminal velocity at the end of the run. Give the answer in miles per hour.
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Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
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Transcribed Image Text:Problem.
You are skiing downhill in Lake Tahoe
Ski Resort. You start from the height
500 m above the lake level and slide 500 m
over the run that makes 30° angle with
respect to horizontal. Initially your speed
is zero.
Lake level
30°
We learned from the last quiz that if you neglect friction and air resistance,
your speed at the end of the run will be as large as 220 mph! Now lets
account for friction and air resistance in your downhill run:
a) What will be your speed at the end of the run if you take into account air
resistance but neglect friction? Assume the drag coefficient 0.6, the air
density is 1.2 kg/m³, the typical mass of a human 80 kg and its cross-
sectional area 0.5 m², and that the skier will reach its terminal velocity at the
end of the run. Give the final answer in miles per hour. Acceleration of
gravity is 9.8 m/s², and 1 mile = 1.609 km.
b) What will be your speed at the end of the run if you now account for
friction between your skis and the snow but neglect air resistance? Assume
the kinetic friction coefficient 0.5. Give the answer in miles per hour.
c) What will be your speed at the end of the run if you take both friction and
air resistance into account? Assume the same data as above and that the skier
will reach its terminal velocity at the end of the run. Give the answer in
miles per hour.
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