Suppose that the speed of light in a vacuum ( c), instead of being a whooping 3\

Question

Suppose that the speed of light in a vacuum ( c), instead of being a whooping 3 imes 10^8; m m/s, was a rather sluggish 40.0 ; m mph. How would that affect everyday life? Throughout this problem we are going to assume that c = 40.0 ; m mph and that time dilation is in full effect. Let's start by assuming that it is fairly easy to accelerate to speeds close to 40.0 ; m mph. We will also ignore gravity throughout this problem. Otherwise, the earth (with an escape velocity of 11; m km/s) would have turned into a black hole long ago.

b. The restaurant the student likes to go to doesn't have any clocks. As a result, the only way that the student can keep track of the time so as not to be late is to keep an eye on her wristwatch. According to the student's watch, how much time does she actually have for lunch if she wants to go to the furthest restaurant (including travel time)?
Express your answer in minutes.

c. Now, suppose the student wishes to bring back some ice cream from the restaurant for her friends at school, but since it is such a hot day, the ice cream will melt away in the car in only 5 minutes. How fast will the student have to drive back to get the ice cream to her friends before it completely melts?
Express your answer in miles per hour.

Please answer fully

Explanation / Answer

Hi, It seems some part of the question is missing. Any way, below expression would be useful in doing your calculation. The expression for time-dilation is given by t = t' (1 - v^2/c^2) here, t will the the time taken according to the student, t' will be the actual time taken as per world clock and v is the velocity with which he travelled and c = 40 mph. Hope this is helpful.

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