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