# A few homework questions

Contraction of length and time: non-science major needs help!

Hey guys, I am in a class on the Quantum Engima @ UCSC. This is a physics class for non-science majors, so being a non-science major I am having a bit of trouble. Right now we're in a special relativity chapter and THIS is on my homework:
4. a) Mary drives from Santa Cruz to Watsonville @ 50mph. Her accurate watch tells her that 1/2 hour has passed during her trip. She calculates the distance (in her reference frame) between two cities. What is the distance she calculates, is she correct? (Hint: since her v<<c her reference frame is for all practical purposes the same as the ground frame)
For this, I just did the simple equation x=rt, 50x1/2=25 miles and I said that in her reference frame, she is correct. However, my teacher isn't one to give us such easy equations and I feel like I need to be using a more relevant equation..
b. Joe drives from Santa Cruz to Watsonville at 50 mph. His INaccurate watch tells him that 1/4 hour has passed during his trip. He calculates the distances between two cities. What is the distance he calculates? Is he correct? (Hint: since his v<<c his reference frame is for all practical purposes the same as the ground frame)
Same here. Did 50x 1/4= 12.5. And concluded that his mileage calculated is incorrect. Again, I'm suspicious. Why did my teacher tell me v<<c?
c. Alien Ig on a fast rocket zips from Santa Cruz to Watsonville at .9 C. Ig's clocks are accurate. Ig calculates the distance between the two cities. What distance does Ig calculate, is Ig correct? (Graph in text can avoid arithmetic) (Hint: t=$$\gamma$$t'
Here I did the equation l=l'/$$\gamma$$ and got 10.77 miles, and that he is correct for his reference frame. However, I don't understand how I could have conceivably avoided arithmetic??

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