Question

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1. Driving around the Earth. The distance around the Earth is very nearly 25,000 miles. Imagine that you could drive a car at 60 miles per hour all the way around the Earth. How long would this take? Express your answer in days. 2. Driving to the Moon. The average distance between the Earth and Moon is 239,000 miles. At 60 mph, how long would a drive to the Moon take? Express your answer in days. 3. Speed of the Earth around the Sun. The Earth orbits the Sun in a nearly circular path with an average radius of 93,000,000 miles. The time required to make one orbit is, by definition, one year (365.25 days). Given this information, calculate the average speed (in miles per hour) of the Earth in its journey around the Sun.

Answer 1

Using the expression

$\text{speed v = } \frac{\text{distance(d)}}{\text{time(t)}}$

we solve the problems

1) The distance (d) = 25000 miles and the speed v = 60 miles per hour

$\text{so the time to cover the distance t = } \frac{d}{v} =\frac{25000}{60} = 416.667 \ hours \\ \\ \text{Now converting hours to days using 24 hours = 1 day} \\ \text {So the time t = } \frac{416.667 \ hours}{1}* \frac{1 \ day}{24 \ hours} = 17.4 \ days$

So, it will take 14.4 days to drive around the earth.

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2) This time the distance = 239000 miles but the speed(v) is still 60 mph. Using these to find the time to drive the distance

$\text{so the time to cover the distance t = } \frac{d}{v} =\frac{239000}{60} = 3983.333 \ hours \\ \\ \text{Now converting hours to days using 24 hours = 1 day} \\ \\ \text {So the time t = } \frac{3983.333 \ hours}{1}* \frac{1 \ day}{24 \ hours} = 165.97 \approx 166 \ days$

So, it will take 166 days to drive to the moon.

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3) The distance traveled by the earth (d) = the circumference of the circular orbit = 2*pi*R

R = radius = 93000000 miles

The earth takes 365.25 days to complete a revolution.

Converting this time to hours, 1 day = 24 hours.

So 365.25 days = (356.25 days) *(24 hours / 1 day) = 8766 hours

$\text{The average speed of the earth = } \\ v= \frac{2\pi R}{t} = \frac{2\pi * 93000000}{8766} = 66659.4 \text{ miles per hour}$

The average speed of the earth = 66659.4 miles per hour.