I need help understanding how to set up the last problem on kinematics? Imagine

Question

I need help understanding how to set up the last problem on kinematics?

Imagine a 4820 kg satellite in a geosynchronous orbit. If an 85.0 kg piece of space junk floats by at a distance of 3.50 m, what force will the space junk feel? 2.23e-6 N

Acceleration of space junk toward the satellite? 2.62e-8 m/s2

Acceleration will the satellite is 4.63e-10 m/s2

Using the above information and what you know about kinematics, how far will the satellite have moved when it encounters the space junk, assuming they meet, each moving with the accelerations you solved for in #10, 11?

Explanation / Answer

here by using the second equation of motion

let the distance covered by the satellite in time t is y

and the distance covered by the space junk in time t is (3.5 - y)

first for the satellite

y = ut + 0.5 * as * t^2

u = 0 m/s

y = 0.5 * as * t^2

t = sqrt( 2 * y / as).....................(1)

then for the space junk

3.5 - y = 0.5 * aj * t^2

t = sqrt((3.5 - y ) * 2 / aj) ................................(2)

then by using both the equations

y * aj = (3.5 - y ) * as

y * aj = 3.5 * as - y * as

y = 3.5 * as / ( aj + as)

y = 3.5 * 4.63 *10^-10 / ( 2.62 * 10^-8 + 4.63 * 10^-10)

y = 0.0607 m

so the satallite move 0.0607 m when it encounters space junk

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