Miranda, a satellite of Uranus, is shown in of the figure below. It can be model

Question

Miranda, a satellite of Uranus, is shown in of the figure below. It can be modeled as a sphere of radius 242 km and mass 6.68 times 10^19 kg. A cliff on Miranda is 5.00 km high. It appears on the limb at the 11 o'clock position in of the figure above and is magnified in part of the figure above. A devotee of extreme sports runs horizontally off the top of the cliff at 8.20 m/s. For what time interval is he in flight? (Ignore the difference in g between the lip and base of the cliff.) s How far from the base of the vertical cliff does he strike the icy surface of Miranda? m What is his vector impact velocity? m/s below the horizontal

Explanation / Answer

(a)

free fall acceleration g = GM/R^2

g = (6.67*10^-11*6.68*10^19)/(242*10^3)^2

g = 0.076 m/s^2

(b)

along vertical

initial velocity voy = 0

acceleration ay = -g = -0.076 m/s^2

displacement y = -5000m

from equation of motion

y = 0.5*ay*t^2

-5000 = -0.5*0.076*t^2

t = 362.7 s

(c)

x = vox*t = 8.2*362.7 = 2974.14 m

(d)

vy = sqrt(2*ay*y)

vy = -sqrt(2*0.076*5000) = -27.76

magnitude = sart(vx^2+vy^2) = sqrt(8.2^2+27.76^2) = 29 m/s

direction = tan^-1(voy/vox) = 73.54 degrees

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