Two manned satellites approaching one another at a relative speed of 0.300 m/s intend to dock. The first has a mass of 4.00 ✕ 103 kg, and the second a mass of 7.50 ✕ 103 kg. Assume that the positive direction is directed from the second satellite towards the first satellite.(a) Calculate the final velocity after docking, in the frame of reference in which the first satellite was originally at rest. ..............m/s

Question
Asked Jun 11, 2019

Two manned satellites approaching one another at a relative speed of 0.300 m/s intend to dock. The first has a mass of 4.00 ✕ 103 kg, and the second a mass of 7.50 ✕ 103 kg. Assume that the positive direction is directed from the second satellite towards the first satellite.

(a) Calculate the final velocity after docking, in the frame of reference in which the first satellite was originally at rest.
 ..............m/s

check_circleExpert Solution
Step 1

Given,

Mass of first satellite, m = 4.00x10 kg
Mass of second satellite, m2 7.50 x 10° kg
Relative velocity between both satellite, v 0.3m/s
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Mass of first satellite, m = 4.00x10 kg Mass of second satellite, m2 7.50 x 10° kg Relative velocity between both satellite, v 0.3m/s

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Step 2

In the frame of the first satellite, if we assume the direction of the approaching velocity of second satellite as positive.

Then, the velocity of both satellites are,

Velocity of first satellite, u = Om/s
Velocity of second satellite,u, 0.3m/s
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Velocity of first satellite, u = Om/s Velocity of second satellite,u, 0.3m/s

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Step 3

After docking both satellite attains equal velocity v.

Applying the conservation of momentu...

ти + т,и, 3D (т, + т,)v
rearranging we get
ти, + ти,
у 3D
т, + т,
(4.00х10' kg)(Om/s)+ (7.50x10* k?) (0.3m/s)
(4.00х10' ke)+(7.50 x10'kg)
=0.196m/s
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ти + т,и, 3D (т, + т,)v rearranging we get ти, + ти, у 3D т, + т, (4.00х10' kg)(Om/s)+ (7.50x10* k?) (0.3m/s) (4.00х10' ke)+(7.50 x10'kg) =0.196m/s

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