Miranda, a satellite of Uranus, is shown in part a of the figure below. It can b
ID: 1500704 • 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 times 1019 kg. Find the free-fall acceleration on its surface. m/s^2 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 4.80 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?Explanation / Answer
a) radius , r = 242 km
r = 2.42 *10^5 m
mass , m = 6.68 *10^19 Kg
let the free fall acceleration on the surface is a
a = G * m/r^2
a = 6.673 * 10^-11 * 6.68 *10^19/(2.42 *10^5)^2
a = 0.0761 m/s^2
the free fall acceleration is 0.0761 m/s^2
b)
let the time of flight is tf
tf = sqrt(2 * h/g)
tf = sqrt(2 * 5000/0.0761)
tf = 362.5 s
the time of flight is 362.5 s
c)
distance from the base of cliff = u * tf
distance from the base of cliff = 4.80 * 362.5 m17
distance from the base of cliff = 1739.8 m
d)
let the imapact velocity is vf
vf = 4.80 i + 0.0761 * 362.5 j
vf = 4.80 i + 27.6 j m/s
vf = sqrt(4.80^2 + 27.6^2) at arctan(27.6/4.80) degree
vf = 28 m/s at 80.13 degree
the vector impact velocity is 28 m/s at 80.13 degree below horizontal