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Miranda, a satellite of Uranus, is shown in part a of the figure below. It can b

ID: 2015124 • Letter: M

Question

Miranda, a satellite of Uranus, is shown in part a of the figure below. It can be modeled as a sphere of radius 242 km and mass 6.68 1019 kg.
(a) Find the free-fall acceleration on its surface.
______ m/s2

(b) A cliff on Miranda is 5.00 km high. It appears on the limb at the 11 o'clock position in part a of the figure above and is magnified in part b of the figure above. A devotee of extreme sports runs horizontally off the top of the cliff at 7.60 m/s. For what time interval is he in flight?
_____s

(c) How far from the base of the vertical cliff does he strike the icy surface of Miranda?
_____m

(d) What is his vector impact velocity?
________m/s _____° below the horizontal

I have tried this problem and am almost out of chances :(

Explanation / Answer

a.

a = Gm/r2

a = (6.6726 x 10-11)(6.68 x 1019)/(242000)2 = .0761 m/s2

b.

y = 1/2 a t2

5000 = 1/2 * .0761 * t2

t = 362.5 s

c.

x = vt

7.60 m/s * 362.5 s = 2755m

d.

v = at = .0761 m/s2 * 362.5 s = 27.58 m/s

tan = 27.58/7.6

= 74.6 degrees below hor

vf = (27.582 + 7.62) = 28.6 m/s