Physics, 02.04.2020 01:31 nyceastcoast

You are designing a ski jump ramp for the next Winter Olympics. You need to calculate the vertical height hh from the starting gate to the bottom of the ramp. The skiers push off hard with their ski poles at the start, just above the starting gate, so they typically have a speed of 2.0 m/sm/s as they reach the gate. For safety, the skiers should have a speed of no more than 30.0 m/sm/s when they reach the bottom of the ramp. You determine that for a 88.0 kgkg skier with good form, friction and air resistance will do total work of magnitude 4000 JJ on him during his run down the slope.

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Answer from: kayla941

50.35 m

Explanation:

Here is the complete question

You are designing a ski jump ramp for the next Winter Olympics. You need to calculate the vertical height (h) from the starting gate to the bottom of the ramp. The skiers push off hard with their ski poles at the start, just above the starting gate, so they typically have a speed of 2.0 m/s as they reach the gate. For safety, the skiers should have a speed of no more than 30.0 m/s when they reach the bottom of the ramp. You determine that for a 85.0 kg skier with good form, friction and air resistance will do total work of magnitude 4000 J on him during his run down the slope.

What is the maximum height (h) for which the maximum safe speed will not be exceeded?

Solution

From work-kinetic energy principles,

work done by gravity on skier, W₁ + work done by friction and air resistance on skier W₂ = kinetic energy change of skier ΔK.

W₁ + W₂ = ΔK

work done by gravity on skier,W₁ = mgh where m = mass of skier = 88.0 kg , g = 9.8 m/s² and h = vertical height of ramp

W₁ = 88 × 9.8h = 862.4h

work done by friction and air resistance on skier, W₂ = -4000 J

kinetic energy change of skier ΔK =¹/₂m(v₂² - v₁²) where v₁ = speed of skier at top of ramp = 2.0 m/s and v₂ = speed of skier at top of ramp = 30.0 m/s

ΔK =¹/₂ × 88(30² - 2²) = 44 × 896 = 39424 J

W₁ + W₂ = ΔK

862.4h + (-4000 J) = 39424 J

862.4h - 4000 J = 39424 J

862.4h = 39424 J + 4000 J

862.4h = 43424 J

h = 43424/862.4 = 50.35 m

So, the maximum height (h) for which the maximum safe speed will not be exceeded is 50.35 m

Answer from: Quest

0.863333

86%

hope this

Answer from: Quest

Is a vector quantity that refers to "the rate at which an object changes its position." imagine a person moving rapidly - one step forward and one step back - always returning to the original starting position. while this might result in a frenzy of activity, it would result in a zero velocity. because the person always returns to the original position, the motion would never result in a change in position. since velocity is defined as the rate at which the position changes, this motion results in zero velocity. if a person in motion wishes to maximize their velocity, then that person must make every effort to maximize the amount that they are displaced from their original position. every step must go into moving that person further from where he or she started. for certain, the person should never change directions and begin to return to the starting position.

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