I need help with problems R1S.8 and R1S.6 in Six Ideas That Shaped Physics Unit

Question

I need help with problems R1S.8 and R1S.6 in Six Ideas That Shaped Physics Unit R: The Laws of Physics Are Frame-Independent by Thomas A. Moore 2nd edition?

R1S.8

A highway patrol officer on the ground uses a radar gun to measure the speed of a suspect's car to be 60 m/s. A patrol car is traveling at 40 m/s relative to the ground, but is moving in the opposite direction as it approaches the car. Assume that the direction in which the suspect is traveling defines the +x direction for everyone.

(a)What object should we choose to be the Home Frame in this problem, according to the conventions established in this chapter?

(b)What object defines the Other Frame?

(c)What object is the object whose velocity we want to determine in both frames?

(d)Calculate the relative velocity of the suspects car and the patrol car.

R1S.6

Imagine that construction crews have set up a pair of blinking lights 60 m apart to make a construction zone along a raod. A car moves along the road with a speed of 30 m/s toward the lights. Let us take the road to be the Home Frame and the car to be the Other Frame.

(a)In the Home Frame, the light farther from the car (light 2) blinks 0.66 s before the other (light 1) blinks as the car approaches both lights. What is the time interval t2'-t1' between the blink events in the car's frame?

(b)What is the X displacement  X2'-X1' between the events in the car frame?

Explanation / Answer

by special relativity, from car frame
time interval = t *? = t/?(1 - (v2/c2)) is alomst equal to 30 sec = 0.66 sec

distance = 30 x 0.66 =19.8 m

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