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The little prince lives on a spherical asteroid with a radius of R=4.0 meters and mass of M=7.0x105 kg (a) Find the escape speed required to escape the gravitational pull of the asteroid. You should derive the equation for the escape speed rather than recalling it from memory. W=d0 5 zF=ma g=9.8m1s 2 dt R=4m R mg M=7.Ox1Okg GM,mz U- 1g2 h-O1xh11 = H m/s (b) The little prince, who has a mass of m=35 kg, jumps off the asteroid with a speed of 1.2 m/s (which is faster than the escape speed) in a direction tangential to the asteroid's surface, as shown in the figure. If the asteroid initially is not rotating. what is its rotational period T (in hours) after the prince jumps off? You can approximate the prince as a point mass on the asteroid's surface, and the asteroid as
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I=Emiriz 3=3 7m+N+3=I R
1.07x10-bs X 60s
tR
N T
h a80000=33a.5+1.2 h7 1118670t=1.2
U=1.
Yg-O1x8L1=7 (c On the figure,sketch the direction of the asteroid's rotation after the little prince jumps off. Also state what is the direction of the angular velocity vector of the asteroid (e.g. to the left, to the right, up the page, down the page, out of the page, into the page).
Ltn