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Write the answers to the following in scientific notation:

a The speed of light in a vacuum is about 2.998 × 108 ms-¹.
Assuming 1 year≈ 365.25 days, determine how far light travels in:
i 1 hour
ii
iii 1 year.
1 day
b How long does it take for light to travel:
i 1 m
ii 1 cm
iii 1 mm?
c In air, light travels at 2.989 x 108 ms-1 and sound travels at 343.2 ms-¹.
How many times faster is light than sound?

User Karolyn
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1 Answer

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Final answer:

The speed of light in a vacuum is about 2.998 x 10^8 m/s. Light travels approximately 1.079 x 10^12 meters in 1 hour, about 2.593 x 10^13 meters in 1 day, and approximately 9.461 x 10^15 meters in 1 year. Sound is about 874,420 times slower than light.


Step-by-step explanation:

To write the speed of light in scientific notation, we can express it as 2.998 x 108 m/s.

i) To determine how far light travels in 1 hour, we can multiply the speed of light by 1 hour in seconds (3600 seconds).
Distance = Speed x Time = 2.998 x 108 m/s x 3600 s = 1.079 x 1012 meters.

ii) To determine how far light travels in 1 day, we can multiply the speed of light by 1 day in seconds (86400 seconds).
Distance = Speed x Time = 2.998 x 108 m/s x 86400 s = 2.593 x 1013 meters.

iii) To determine how far light travels in 1 year, we can multiply the speed of light by 1 year in seconds (365.25 days x 86400 seconds).
Distance = Speed x Time = 2.998 x 108 m/s x (365.25 days x 86400 s) = 9.461 x 1015 meters.

b) i) To determine how long it takes for light to travel 1 meter, we can divide the distance by the speed of light.
Time = Distance / Speed = 1 meter / 2.998 x 108 m/s = 3.335 x 10-9 seconds.

ii) To determine how long it takes for light to travel 1 centimeter, we can convert centimeters to meters and then divide the distance by the speed of light.
Time = Distance / Speed = 0.01 meter / 2.998 x 108 m/s = 3.336 x 10-11 seconds.

iii) To determine how long it takes for light to travel 1 millimeter, we can convert millimeters to meters and then divide the distance by the speed of light.
Time = Distance / Speed = 0.001 meter / 2.998 x 108 m/s = 3.336 x 10-12 seconds.

c) To determine how many times faster light is than sound, we can divide the speed of light by the speed of sound.
Speed ratio = Light Speed / Sound Speed = (2.998 x 108 m/s) / 343.2 m/s = 874,420 times faster.


Learn more about Scientific notation and speed of light

User Hugo Demiglio
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