Long Trips at Constant Acceleration: Spaceship sider again the spaceship from Problem 55 on a long trip with a constant acceleration of 1g. As long as the ship is gone from Earth for many years, the amount of time that passes on the spaceship during the trip turns out to be approximately те. 20 g × D tship

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Chapter3: Two-dimensional Kinematics
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- Long Trips at Constant Acceleration: Spaceship Time. Con-
sider again the spaceship from Problem 55 on a long trip
with a constant acceleration of 1g. As long as the ship is gone
from Earth for many years, the amount of time that passes on
the spaceship during the trip turns out to be approximately
20
g × D
tship
In
where D is the distance to the destination and In stands
for the natural logarithm (which you can calculate with the
"In" key on most scientific calculators). If D is in meters,
g = 9.8 m/s², and c = 3 × 10° m/s, the answer will be in
units of seconds. Use the formula to determine how much time
will pass on the ship during its trip to a star that is 500 light-
years away. Compare this to the amount of time that will pass
on Earth. (Hint: Be sure you convert the distance from light-
years to meters and your answer from seconds to years.)
Transcribed Image Text:- Long Trips at Constant Acceleration: Spaceship Time. Con- sider again the spaceship from Problem 55 on a long trip with a constant acceleration of 1g. As long as the ship is gone from Earth for many years, the amount of time that passes on the spaceship during the trip turns out to be approximately 20 g × D tship In where D is the distance to the destination and In stands for the natural logarithm (which you can calculate with the "In" key on most scientific calculators). If D is in meters, g = 9.8 m/s², and c = 3 × 10° m/s, the answer will be in units of seconds. Use the formula to determine how much time will pass on the ship during its trip to a star that is 500 light- years away. Compare this to the amount of time that will pass on Earth. (Hint: Be sure you convert the distance from light- years to meters and your answer from seconds to years.)
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