Question

The planet Mercury has a radius of 1500 miles and rotates one revolution every 1400 hours. What is the linear speed of a point on its equator in miles per hour?

Answer 1

Answer:

$V = w C = 0.004488 \frac{rad}{hr} *3000 \pi mi = 42.298 \frac{mi}{hr}$

Step-by-step explanation:

If we are in the equator we can assume a circular pattern and we can find the angular velocity like this:

$w = \frac{1 rev}{1400 hr} *\frac{2\pi rad}{1 rev}= 0.004488 rad/hr$

After we have this we can find the total distance travelled finding the circumference length of the planet Mercury at the equator with the following formula:

$C = 2 \pi R$

And we can replace the values given and we got:

$C = 2\pi *1500 mi =3000 \pi mi$

Now we can find the linear speed using this formula between the circumference and the angular velocity:

$V = w C = 0.004488 \frac{rad}{hr} *3000 \pi mi = 42.298 \frac{mi}{hr}$

And that would be the linear velocity required for this case.