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Two manned satellites approaching one another at a relative speed of 0.550 m/s intend to dock. The first has a mass of 2.50 ✕ 103 kg, and the second a mass of 7.50 ✕ 103 kg. If the two satellites collide elastically rather than dock, what is their final relative velocity? Adopt the reference frame in which the second satellite is initially at rest and assume that the positive direction is directed from the second satellite towards the first satellite. .............m/s

Question

Two manned satellites approaching one another at a relative speed of 0.550 m/s intend to dock. The first has a mass of 2.50 ✕ 103 kg, and the second a mass of 7.50 ✕ 103 kg. If the two satellites collide elastically rather than dock, what is their final relative velocity? Adopt the reference frame in which the second satellite is initially at rest and assume that the positive direction is directed from the second satellite towards the first satellite.
 .............m/s

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Step 1

Let m1 and m2 be the mass of first and second satellite respectively.

Assuming the initial velocity of first satellite be v and that of second satellite be u.

Here, it is mentioned that the second satellite is assumed to be at rest initially, and the direction from the second satellite to the first one is taken as positive.

As both the satellites are approaching towards each other, so the relative velocity of first satellite with respect to second satellite is vr=(-v)-u and that of second satellite with respect to itself is ur=u-u=0.

 

Step 2

The information given in the question is as follows,

- 2.5 x 10 kg
m, =7.5 x10 kg
,-0.550 m/s
u 0 m/s
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Image Transcriptionclose

- 2.5 x 10 kg m, =7.5 x10 kg ,-0.550 m/s u 0 m/s

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Step 3

Now, the collision is elastic and relative final velocities of satellites 1 and 2 are taken to be vf1 and vf2 respectively....

2m2
|и,
"л
т, + т,
ш- ш
т, + т,
2m2
т, — т,
|и,
т, + т,
т + т,
help_outline

Image Transcriptionclose

2m2 |и, "л т, + т, ш- ш т, + т, 2m2 т, — т, |и, т, + т, т + т,

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