Answer:
[tex] V = w C = 0.004488 \frac{rad}{hr} *3000 \pi mi = 42.298 \frac{mi}{hr}[/tex]
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:
[tex] w = \frac{1 rev}{1400 hr} *\frac{2\pi rad}{1 rev}= 0.004488 rad/hr[/tex]
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:
[tex] C = 2 \pi R[/tex]
And we can replace the values given and we got:
[tex] C = 2\pi *1500 mi =3000 \pi mi [/tex]
Now we can find the linear speed using this formula between the circumference and the angular velocity:
[tex] V = w C = 0.004488 \frac{rad}{hr} *3000 \pi mi = 42.298 \frac{mi}{hr}[/tex]
And that would be the linear velocity required for this case.
