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A speed of 1/4 m/s is split into two components along OA and OB, where OA and OB make angles of 30° and 45°, respectively, with the given velocity. The magnitude of the component along OB is

1. 1/8 (√6 − √2) m/s
2. 1/4 (√3 − 1) m/s
3. 1/4 m/s
4. 1/8 m/s

Correct answer: 1/8 (√6 − √2) m/s

Solution

The correct option is derived from resolving the velocity vector into its components along OA and OB using trigonometric functions. By applying the sine of the angle for OB, we find that the magnitude of the component along OB is indeed 1/8 (√6 − √2) m/s, which accurately represents the projection of the original speed in that direction.

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