Time Dilation. a. A learning about the relativity, decides to apply his knowledg
ID: 1614686 • Letter: T
Question
Time Dilation. a. A learning about the relativity, decides to apply his knowledge in order to prolong his life. He decides to spend the rest of his life in a car, traveling around the freeways at 55 miles per hour (89 km/hr). Suppose he drives for a period of time during which 70 years pass in his house. How much time will pass in the car? b. An even more clever student decides to prolong her life by cruising around the local solar neighborhood at a speed of 0.95c (95% the speed of light). How much time will pass on her spacecraft during a period in which 70 years pass on Earth? Will she feel as if her life span has been extended? Explain. c. Suppose you stay home on Earth while your twin sister takes a trip to a distant star and back in a spaceship that travels at 99% of the speed of light. If both of you are 25 years old when she leaves and you are 45 years old when she returns, how old is your sister when she gets back?Explanation / Answer
46
a)
v = 89 km/hr = 24.72 m/s
c = speed of light = 3 x 108 m/s
T = time passexd in house = 70 yrs
To = time passed in car = ?
using the formula
T = To/sqrt(1 - (v/c)2)
70 = To/sqrt(1 - ((24.72)/(3 x 108))2)
To = 70 yrs
this is due to to the fact that the time dilation takes place at speed comparable to speed of light . herce speed of car is very small to notice any change in time .
b)
v = 0.95 c
c = speed of light = 3 x 108 m/s
T = time passed at earth = 70 yrs
To = time passed in car = ?
using the formula
T = To/sqrt(1 - (v/c)2)
70 = To/sqrt(1 - (0.95)2)
To = 21.85 yrs
c)
v = 0.99 c
c = speed of light = 3 x 108 m/s
T = time passed at earth = 45 - 25 = 20 yrs
To = time passed in spaceship = ?
using the formula
T = To/sqrt(1 - (v/c)2)
20 = To/sqrt(1 - (0.99)2)
To = 2.82 yrs
age of sister = 25 + 2.82 = 27.82 yrs
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