Suppose you\'re driving down the highway at a speed of 25 m/s. A truck in the ne

Question

Suppose you're driving down the highway at a speed of 25 m/s. A truck in the next lane is traveling toward you with a speed of 35 m/s relative to the ground. Relative to you the truck is approaching at a speed of 25 m/s + 35 m/s = 6.0 x 101 m/s.

a) Since the speeds are much less than the speed of light, would the relative speed be the same if you were going 5.0 m/s relative to the ground and the truck were moving at 55 m/s relative to the ground? Give a reason for your answer.

b) Suppose the speed of light were c=65 m/s. Would the relative speeds be the same for the two situations? Give a reason for your answer.

c) Using the data presented above and assuming the speed of light is c = 65 m/s, determine the speed of the truck relative to you for the two situations when your speed and the truck's spare are, respectively, 25 m/s and 35 m/s, and

d) 5.0 m/s and 55 m/s.

Explanation / Answer

a)

yes relative speed will be same

as the car and truck are travelling in opposite direction

relative speed = speed of car + speed of truck = 5 + 55 = 60 m/s

b)

the relative speed will be difference since the speed of car and truck are now comparable with the speed of light and we can not simply add the velocities to get the relative speed

c)

Vc = velocity of car = 25c/65 = 0.385 c

Vt = velocity of truck = 35c/65 = 0.538c

relative speed = (Vt - Vc )/ (1 - Vt Vc /c2) = (0.538c - 0.385c) / (1 - (0.385) (0.538)) = 0.193 c = 0.193 x 65 = 12.55

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