A disc rotates about a spindle with a constant angular velocity $=2\mathrm{.}1ra\frac{d}{s},$ as shown in the figure. A spacecraft orbits the Earth unpowered in a circular path at a height of $314$ km above the Earth's surface, as shown in the figure.

At position A thrusters are applied briefly that DOUBLE the satellite's speed.

You may assume:

$R_E=6,380,000m$;$M_E=5\mathrm{.}98E24kg$ and $G=6\mathrm{.}673E-11N.\frac{m^2}{k}{g}^2$

What is the period the spacecraft before the thrusters are applied?

What is the angular velocity of the craft at B with respect to the Earth's centre, ${}_B,$ when the radius has increased by $19\mathrm{.}1\%$ from the circular orbit radius?

A small block is situated in a frictionless slot at a radius of $r_0=0\mathrm{.}21m,$ where it is initally at rest with respect to the disc.

The outer radius of the disc is $R=1\mathrm{.}38m.$

If the block is allowed to slide freely one imagines that it will slide outward past the outer edge of the disc.

What is the magnitude of the block's velocity as it passes across the outer edge of the disc?

Hint: This is just tricky. No other way to put it really! There is NO FORCE in the radial direction, but there will be a "centrifugal effect". Remember that the final

velocity will have radial and transverse components!