A newly discovered planet has a mean radius of 4.70 times 103 km. A vehicle on t

Question

A newly discovered planet has a mean radius of 4.70 times 103 km. A vehicle on the planet's surface is moving in the same direction as the planet's rotation, and its speedometer reads 113 km/h. If the angular velocity of the vehicle about the planet's center is 9.03 times as large as the angular velocity of the planet, what is the period of the planet's rotation? If the vehicle reverses direction, how fast must it travel (as measured by the speedometer) to have an angular velocity that is equal and opposite to the planet's?

Explanation / Answer

V=113 km/h=31.39 m/s

V=Vv+Vp=31.39

   Vv=velocity of veichle Vp= velocity of plannet

now wv=wp

Vv*r=9.03*Vp*r

solving for Vv and Vp we get

Vp=3.12 m/s

Vv=28.26 m/s

T=2*pi*r/Vp

=9.46*10^6 s

=109.54 days

b.)v1/r1=v2/r2

v1=3.12 m/s

so V=Vp+Vv

Vp=-3.12 m/s

V=0 as measured by speedometer

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