The planet Tralfamador is a planet of mass M and radius R, and very thin atmosph

Question

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 gun with an unknown speed v0 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 v0 in m/s.

B) Find the launch angle theta.

DETAILED ANSWERS PLEASE!!

Thank you!

Explanation / Answer

a)Ei = Ef

1/2 mv^2 - G M m/R = 1/2 mv^2 - G M m/(5 R/4)

1/2*v^2 - 1.0E10/200.0E3 = 0.5*75^2 - 1.0E10/(5*200.0E3/4)

v=160 m/s

b)

so vx doesnt change

so cos theta= 75/160

theta = arcos(75/160)=62.05 degrees

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