Question Video: Calculating the Relative Velocity of a Particle with Respect to Another Particle

If 𝐕_(π‘Žπ‘) =20𝐒 and 𝐕_(π‘Ž) = 45𝐒, then 𝐕_(𝑏) = _𝐒.

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Video Transcript

If 𝐕 sub π‘Žπ‘ is equal to 20𝐒 and 𝐕 sub π‘Ž equals 45𝐒, then 𝐕 sub 𝑏 is equal to what 𝐒.

In this question, we are given the relative velocity of π‘Ž with respect to 𝑏 in terms of the unit vector 𝐒. We are also given the velocity of π‘Ž in terms of the unit vector 𝐒. And we need to calculate the velocity vector 𝑏.

We recall that the velocity of π‘Ž relative to 𝑏 is the velocity of π‘Ž minus the velocity of 𝑏 for two bodies π‘Ž and 𝑏 moving along the same one-dimensional axis. Substituting in the values we are given, we have 20𝐒 is equal to 45𝐒 minus the velocity of 𝑏. By adding the velocity of 𝑏 and subtracting 20𝐒 from both sides of our equation, we have the velocity of 𝑏 is equal to 45𝐒 minus 20𝐒. This is equal to 25𝐒. The missing number in the question is 25.

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