To find the ratio of planetary speeds Va/Vb we need the orbital velocity formula:
V=√({G*M}/R), where G is the gravitational constant, M is the mass of the distant star and R is the distance of the planet from the star it is orbiting.
So Va/Vb=[√( {G*M}/Ra) ] / [√( {G*M}/Rb) ], in our case Ra = 7.8*Rb
Va/Vb=[ √( {G*M}/{7.8*Rb} ) ] / [√( {G*M}/Rb )], we put everything under one square root by the rule: (√a) / (√b) = √(a/b)
Va/Vb=√ [ { (G*M)/(7.8*Rb) } / { (G*M)/(Rb) } ], when we cancel out G, M and Rb we get:
Va/Vb=√(1/7.8)/(1/1)=√(1/7.8)=0.358 so the ratio of Va/Vb = 0.358.
I believe that you would weigh around 68 or 69 N, or 7 kilograms.
Answer:
The problem occurs with all spherical mirrors.
Spherical mirrors are practical up to about inches in diameter.
Reflecting telescopes use spherical mirrors for apertures up to about 4 ".
Larger aperture telescopes use parabolic mirrors to obtain sharp focus.
Solving for acceleration:
F = ma
10000 = 2000*a
a = 5 m/s^2
Solving for velocity:
Vf = Vi + a(t)
0 = Vi - (5)(6)
Vi = 30 m/s
Solving for displacement or distance:
S = Vi*t - 1/2 * a * t^2
S = 30(6) - 1/2 (5)(6)^2
S = 90m
The car would have traveled 90m before coming to rest.