SOLUTION: The speed of light is 300,000km/sec and the planet Pluto is located at a distance of 6 billion km from Earth. If a spaceship, traveling at a constant speed in a straight line, goes
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Question 1205494: The speed of light is 300,000km/sec and the planet Pluto is located at a distance of 6 billion km from Earth. If a spaceship, traveling at a constant speed in a straight line, goes from Earth to Pluto in 100 hours, at what fraction of the speed of light is this spaceship travelling? Thank You!
Found 3 solutions by greenestamps, math_tutor2020, josgarithmetic:
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!
100 hours = 100*60 minutes = 100*60*60 seconds.
Divide the distance of 6 billion km by that number of seconds to find the speed of the spaceship in km/sec.
Divide that speed by the speed of light (both in km/sec) to get the answer.
You can do the calculations; use a calculator if needed.
ANSWER: You should get an answer of 1/18....
Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!
300,000 = 3*10^5
6 billion = 6*10^9
1 hour = 60*60 = 3600 seconds
100 hours = 100*3600 = 360,000 seconds
360,000 = 3.6*10^5
Determine the speed of the spaceship
distance = rate*time
rate = distance/time
rate = (6*10^9 km)/(3.6*10^5 seconds)
rate = (6/3.6)*((10^9)/(10^5)) km per second
rate = (60/36)*10^4 km per second
rate = (5/3)*10^4 km per second
Divide this over the speed of light to wrap things up
( spaceship's speed )/( speed of light )
( (5/3)*10^4 )/( 3*10^5 )
( (5/3)*10^4 )/( 3*10*10^4 )
( (5/3)*10^4 )/( 30*10^4 )
( (5/3)/30 )*((10^4)/(10^4))
(5/3)/30
(5/3)*(1/30)
5/90
1/18 is the final answer.
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Another approach
Let's see how long it takes a light beam to go from Earth to Pluto
distance = rate*time
time = distance/rate
time = (6*10^9 km)/(3*10^5 km per sec)
time = (6/3)*((10^9)/(10^5)) sec
time = 2*10^4 sec
time = 20,000 sec
Divide this over 360,000 seconds (the time it takes the spaceship to reach Pluto) and you should get the fraction 1/18
It represents the idea that the light beam can travel to Pluto 18 times in the same timespan the spaceship travels.
In other words, the light beam travels 18/2 = 9 round trips from Earth to Pluto, and back. In these 9 round trips of the light beam, the spaceship will arrive at Pluto.
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Answer: 1/18
Answer by josgarithmetic(39618) (Show Source): You can put this solution on YOUR website!
THE SPACESHIP
COMPARE TO LIGHT SPEED
0.0555555555555...
---------as fraction of speed of light
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