can someone help me with this quesstion Suppose you have a fire truck 9.0 m long

Question

can someone help me with this quesstion

Suppose you have a fire truck 9.0 m long that is capable of going very fast. If the fire truck drives by you at a speed of 0.85c (i.e., 85% of the speed of light), how long is it in your reference frame? A fire starts in a house 4.0 km away from the firehouse - but an easy drive down a straight road. The fire fighters immediately drive the truck along the road at a constant speed of 0.85c . How long do the occupants of the binning house have to wait (according to their clock) for the fire truck to arrive? In the fire truck's frame of reference, it is not moving (!), while the road and burning house are moving toward it at a speed of 0.85c . Considering length contraction, how long is the road to the binning house in the fire truck's frame of reference? And how long does it take the fire fighters to drive that distance, according to the clock on board the fire truck? The fire truck is bright red, with a peak wavelength of 660 nm. However, when the occupants of the burning house see it coming toward them, it appears different. What is the peak wavelength that the occupants of the binning house see? And how could you describe that as a color?

Explanation / Answer

a) Length = L*sqrt(1 - (v/c)^2 ) = 9* 0.526 = 4.74 m

b)Time Of Wait = 4/(0.85c) = 15.7 micro seconds

c) L*sqrt(1 - (v/c)^2 ) = 4 * 0.526 =2.1 km

15.7 micro s * 1/0.526 = 29.8 micro s

d) v/c = B

f1/f2 = sqrt((1+B)/(1-B))

f1 = 2310 nm

This is beyond the visible spectrum.

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