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.

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

scattering of light by tiny particles in air to produce the colors we see on sky, is dependent on the following factors:

(i) wavelength of light

(ii) size of the scattering particle  

(iii) distance traveled by light through the atmosphere.

according to rayleigh's law of scattering, the amount of scattering is inversely proportional to the fourth power of its wavelength. shorter the wavelength, greater is its scattering. hence violet/blue light is scattered more than red.

sun's light is a composite light ( visible light) with wavelengths in the range 400 nm (violet) to 700 nm (red). as sunlight passes through our atmosphere, the molecules of air scatter light according to their wavelengths. during sunrise and sunset, the sun's position is below the horizon. hence light from the sun travels a greater distance in the atmosphere when compared to its position a noon.

as sunlight enters the earth's atmosphere, blue light is scattered away and at the end of its journey in the sky, only red and orange wavelengths remain in the beam.

hence at sunrise and sunset, the sky appears reddish orange.