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Posted by **Oriana** on Tuesday, December 14, 2010 at 5:24pm.

(b) How far from the surface will a particle go if it leaves the asteroid's surface with a radial speed of 1000 m/s?

(c) With what speed will an object hit the asteroid if it is dropped from 1000 km above the surface?

I know how to do the first question (conservation of mechanical energy): however, I have no idea how to do the other two problems

- College Physics w/Calculus -
**drwls**, Tuesday, December 14, 2010 at 6:23pm(a) Potential enegy increase = -M*Integral of g(r) dr (R to infinity) = -M*g(R)*R^2/r^2 dr

= M*g(R)/R = (1/2) M Vo^2

Vo = sqrt(2g(R)*R)

= 1880 m/s

is the escape velocity

(b) PE change = M*[g(R)*R^2(1/R - 1/r) g(R)*R/r]

= (1/2) M V^2

2 g(R)* R^2 (1/R - 1/r) = V^2

2g(R)*R - V^2 = 2g(R)*R^2/r

= 3.53*10^6 - 10^6 m^2/s^2 = 2.53*10^6 m^2/s^2

r = 2*(3.1 m/s^2)(570*10^3)^2 m^2/2.53*10^6 m^2/s^2

= 7.96*10^5 m

= 796 km. Subtract the asteroid radius (570 km) from that to get the altitude above the surface

(c) The kinetic energy at R will equal the PE decrease in going from R + 1000 km to R altitude

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