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An object has velocity relative to the ground. An observer moving past with a constant velocity relative to the ground measures the velocity of the object to be (relative to the observer). The magnitudes of these velocities are related by (A) v 0 ≤ v 1 + v 2 . (B) v 1 ≤ v 2 + v 0 . (C) v 2 ≤ v 0 + v 1 . (D) All the above are true.

An object has velocity  relative to the ground. An observer moving past with a constant velocity  relative to the ground measures the velocity of the object to be  (relative to the observer). The magnitudes of these velocities are related by
(A) v0 ≤ v1 + v2.                                        (B) v1 ≤ v2 + v0.
(C) v2 ≤ v0 + v1.                               
(D) All the above are true.
 

Grade:11

1 Answers

Aditi Chauhan
askIITians Faculty 396 Points
9 years ago
The correct option is: (C) v2 < v0 + v1.
The object moving with velocity \overrightarrow{v_{o}}relative to ground observe the maximum velocity of object moving with velocity\overrightarrow{v_{1}} , when both objet move in the opposite direction relative to each other such that
v2 = v0 + v1
For any other direction of motion between object moving with velocity \overrightarrow{v_{0}}and object moving with velocity \overrightarrow{v_{1}}, the relative speed as observed by the object moving with velocity \overrightarrow{v_{1}}will be less than v0 + v1 .
Therefore, the magnitude of velocity of object moving with velocity \overrightarrow{v_{0}}relative to the object moving with velocity\overrightarrow{v_{1}} will always be less than or equal to the sum of their velocity with respect to ground, that is
v2 \leq v0 + v1
Therefore, (C) is the correct option and the rest are ruled out.



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