Atourist being chased by an angry bear is running in a straight line toward his car at a speed of 3.8 m/s. the car is a distance d away. the bear is 22 m behind the tourist and running at 6.3 m/s. the tourist reaches the car safely. what is the maximum possible value for d?

The maximum possible value for d is 33.4 m.

The bear chases the tourist with a speed v₁ and the tourist runs with a speed v₂. The distance between the tourist and the car is d and the distance between the tourist and the bear is 22 m. for the tourist to reach the car safely, he should cover the distance d in the same time as the bear, which covers a distance d+22 m.

Therefore,

Substitute 3.8m/s for v₂ and 6.3 m/s for v₁. Solve for d.

The maximum distance between the tourist and his car, for him to be safe from the chasing bear is 33.4 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.