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An object has velocity ${\vec{v}}_{1}$ w.r.t. ground. An observer moving with constant velocity ${\vec{v}}_{0}$ w.r.t. ground measures the velocity of the object as ${\vec{v}}_{2}$ . The magnitudes of three velocities are related by

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a

$v_{0} \geq v_{1} + v_{2}$

b

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

c

$v_{2} \geq v_{1} + v_{0}$

d

All of the above

answer is B.

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Detailed Solution

${\vec{v}}_{2} = {\vec{v}}_{1} - {\vec{v}}_{0}, {\vec{v}}_{2} + {\vec{v}}_{0} = {\vec{v}}_{1}$

From the law of triangle, we can draw the velocity vector diagram (figure) .

Question Image

From triangle property, sum of two sides $\geq$ third side. So $v_{1} \leq v_{0} + v_{2}$

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An object has velocity v→1 w.r.t. ground. An observer moving with constant velocity v→0 w.r.t. ground measures the velocity of the object as v→2 . The magnitudes of three velocities are related by