A 70 kg skydiver falls from an altitude of 10 km to 1 km before pulling their parachute. They are unmoving when they leap out of their plane. Neglecting air resistance, what is the skydiver’s velocity when they pull the chute? How much work must be done by the parachute to slow the skydiver to 1 m s−1 at the ground level

a) 420.2 meters per second

b) --6179846.4 joules

Explanation:

Using conservation of energy:

with Ki the initial kinetic energy, Kf the final kinetic energy, Ui the initial potential energy and Uf the final potential energy.

(2)

With Vi the initial velocity, Vf the final velocity, m the mass of the skydiver , g the gravitational acceleration, hi the initial altitude and hf the final altitude

Solving (2) for Vf:

Vi is zero because they are unmoving when they leap out of their plane, hi is 10km and hf is 1 km:

By work-energy theorem:

with W the total work and ΔK the change on kinetic energy and Kg kinetic energy at ground level

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.