In Example 2.5, we noted that Anna could go wherever she wished in as little time as desired by going fast enough to length−contract the distance to an arbitrarily small value. This overlooks a physiological limitation. Accelerations greater than about 30g are fatal, and there are serious concerns about the effects of prolonged accelerations greater than 1g. Here we see how far a person could go under a constant acceleration of 1g, producing a comfortable artificial gravity. (a) Though traveler Anna accelerates, Bob, being on near−inertial Earth, is a reliable observer and will see less time go by on Anna’s clock ( d t ' ) than on his own ( d t ) . Thus, d t ' = ( 1 / γ u ) d t , where u isAnna’s instantaneous speed relative to Bob, Using the result of Exercise 117(c), with g replacing F / m , substitute for u , then integrate to show that t = c g sinh g t ' c (b) How much time goes by for observes on Earth as they “see” Anna age 20 years? (c) Using the result of Exercise 119, show that when Anna has aged a time t ' . She is a distance fromEarth (according to Earth observers) of x = c 2 g ( cosh g t ' c − 1 ) (d) If Anna accelerates away from Earth while aging 20 years and then slows to a stop while aging another 20, how far away from Earth will she end up, and how much time will have passed on Earth?
In Example 2.5, we noted that Anna could go wherever she wished in as little time as desired by going fast enough to length−contract the distance to an arbitrarily small value. This overlooks a physiological limitation. Accelerations greater than about 30g are fatal, and there are serious concerns about the effects of prolonged accelerations greater than 1g. Here we see how far a person could go under a constant acceleration of 1g, producing a comfortable artificial gravity. (a) Though traveler Anna accelerates, Bob, being on near−inertial Earth, is a reliable observer and will see less time go by on Anna’s clock ( d t ' ) than on his own ( d t ) . Thus, d t ' = ( 1 / γ u ) d t , where u isAnna’s instantaneous speed relative to Bob, Using the result of Exercise 117(c), with g replacing F / m , substitute for u , then integrate to show that t = c g sinh g t ' c (b) How much time goes by for observes on Earth as they “see” Anna age 20 years? (c) Using the result of Exercise 119, show that when Anna has aged a time t ' . She is a distance fromEarth (according to Earth observers) of x = c 2 g ( cosh g t ' c − 1 ) (d) If Anna accelerates away from Earth while aging 20 years and then slows to a stop while aging another 20, how far away from Earth will she end up, and how much time will have passed on Earth?
In Example 2.5, we noted that Anna could go wherever she wished in as little time as desired by going fast enough to length−contract the distance to an arbitrarily small value. This overlooks a physiological limitation. Accelerations greater than about 30g are fatal, and there are serious concerns about the effects of prolonged accelerations greater than 1g. Here we see how far a person could go under a constant acceleration of 1g, producing a comfortable artificial gravity. (a) Though traveler Anna accelerates, Bob, being on near−inertial Earth, is a reliable observer and will see less time go by on Anna’s clock
(
d
t
'
)
than on his own
(
d
t
)
. Thus,
d
t
'
=
(
1
/
γ
u
)
d
t
, where u isAnna’s instantaneous speed relative to Bob, Using the result of Exercise 117(c), with g replacing
F
/
m
, substitute for u, then integrate to show that
t
=
c
g
sinh
g
t
'
c
(b) How much time goes by for observes on Earth as they “see” Anna age 20 years? (c) Using the result of Exercise 119, show that when Anna has aged a time
t
'
. She is a distance fromEarth (according to Earth observers) of
x
=
c
2
g
(
cosh
g
t
'
c
−
1
)
(d) If Anna accelerates away from Earth while aging 20 years and then slows to a stop while aging another 20, how far away from Earth will she end up, and how much time will have passed on Earth?
A train upon passing point A at a speed of 72 kph accelerates at 0.75 m/s2 for 1 minute along a straight path then decelerates at 1.0 m/s2. How far in kilometers from point A will it be 2 minutes after passing point A. (Please make the solution easy to understand, thank youu)
*59. ssm Consult Multiple-Concept Example 8 to explore a model for
solving this problem. (a) Just for fun, a person jumps from rest from
the top of a tall cliff overlooking a lake. In falling through a distance H,
she acquires a certain speed v. Assuming free-fall conditions, how much
farther must she fall in order to acquire a speed of 2v? Express your
answer in terms of H. (b) Would the answer to part (a) be different if
this event were to occur on another planet where the acceleration due to
gravity had a value other than 9.80 m/s²°? Explain.
A downhill skier crosses the finishing line at a speed of 30 m/s and immediately starts to decelerate at 10 m/s2 . There is a barrier 50 meters beyond the finishing line.
(a) Find an expression for the skier s speed when she is V meters beyond the finishing line.
(b) How fast is she travelling when she is 40 meters beyond the finishing line?
(c) How far short of the barrier does she come to a stop?
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