The planet Tralfamador is a planet of mass M and radius R, and very thin atmosphere (neglect air resistance). A magnetic rail gun has been mounted on the surface of Tralfamador at the North pole. A projectile of mass m is fired from the magnetic rail of gun with an unknown speed V.o at an unknown angle theta with respect to the local horizontal. The projectile is observed to rise to a maximum height above the surface of 1/4 R. At this maximum height the projectile has a speed of 75.0 m/s.
A) If M= 1.5 x 10^20 kg (so that GM= 1.0 x 10^10 Nm^2/kg) and R= 200 km, find V.o in m/s.
B) Find the launch angle theta. (If you don't know how to do (A) you may show how to find theta as if you knew V.0)
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