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