An object has velocity V 1 relative to the ground- An observer moving with a constant velocity v 0 relative to the ground measures the velocity of the objectto be V 2 relative to the observer- The magnitude of these velocities is related by where v 0- v 1 and v 2 are their respective magnitudesA- v 0- v 1- v 2B- v 1- v 2- v 0C- v 2- v 0- v 1D- All the above are true

The correct option is C v_2 ≤ v_0+v_1The observer moving with velocity v_o nbsp;relative to ground observes the maximum velocity of the object moving with ...

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Standard XII

Physics

Relative Velocity

An object has...

Question

An object has velocity $_{1}$ relative to the ground. An observer moving with a constant velocity $_{0}$ relative to the ground measures the velocity of the object to be $_{2}$ (relative to the observer). The magnitude of these velocities is related by (where $v_{0}, v_{1}$ and $v_{2}$ are their respective magnitudes)

v_{0} \leq v_{1} + v_{2}

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v_{1} \leq v_{2} + v_{0}

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v_{2} \leq v_{0} + v_{1}

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All the above are true

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Solution

The correct option is C $v_{2} \leq v_{0} + v_{1}$
The observer moving with velocity $_{o}$ relative to ground observes the maximum velocity of the object moving with velocity $_{1}$ , when both the object moves in the opposite direction relative to each other i.e. $\to v_{2} =_{1} - (-_{0}) = \to v_{1} +_{0}$
For any other direction of motion between object moving with velocity $_{0}$ and object moving with velocity $_{1}$ , the magnitude of relative velocity observed by the object moving with velocity $v_{1}$ will be less than $v_{0} + v_{1}$ .

Thus the magnitude of velocity of object moving with velocity $_{0}$ relative to the object moving with velocity $_{1}$ will always be less than or equal to the sum of their velocity with respect to ground, that is
$v_{2} \leq v_{0} + v_{1}$
Hence, the correct answer is option (C)

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