Question

Three vehicles A,B and C are moving a long straight line in space in the same direction the objectives is for vehicle C to dock with vehicle B, if  east and  east how long is is it to docking if the vehicles B and C are 100,000 meter a parts.

Answer 1

Suppose the velocity of vehicle B be $\vec{v}$_B due east and the velocity of vehicle C be $\vec{v}$ _C due east.

Relative velocity of C with respect to B, $\vec{v}$_CB=$\vec{v}$_c-$\vec{v}$_B due east.

Thus to a passenger in vehicle B, the vehicle C will appear to move towards it (due east) with a velocity of $\vec{v}$_CB .

The vehicle C will move with $\vec{v}$_CB to cover 100,000 meter separation between it and the vehicle B so as to dock with vehicle B.Here in the question the magnitudes of the velocities of vehicles B and C is not given.Let us assume that $\vec{v}$_CB =100m/sec.

The time that would be taken by vehicle C to dock with vehicle B will be given by

$time\space taken\space by\space vehicle\space C\space to\space dock\space k\space with\space vehicle\space B= \frac{distance\space by\space which \space vehicle\space C \space is \space separated\space from \space vehicle\space B}{relative \space velocity \space of \space Vehicle\space C\space with\space respect\space to\space vehicle\space B}$

$time\space taken=\frac{100,000}{100}=1000\space seconds\space or\space 16.67 min$

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