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

Fill in the blank. If 𝐕_(𝑎𝑏) = 25𝐢 and 𝐕_𝑎 = 40𝐢, then 𝐕_𝑏 = ＿ 𝐢.

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### Video Transcript

Fill in the blank. If 𝐕 sub 𝑎𝑏 is equal to 25𝐢 and 𝐕 sub 𝑎 is equal to 40𝐢, then 𝐕 sub 𝑏 is equal to what 𝐢.

In this question, we are given the relative velocity of 𝑎 with respect to 𝑏 in terms of the unit vector 𝐢. We are also given the velocity of 𝑎 in terms of the unit vector 𝐢. And we are asked to find the coefficient of 𝐢 in 𝐕 sub 𝑏.

We know that both bodies are traveling in the same direction, and the velocity of 𝑎 relative to 𝑏 is equal to the velocity of 𝑎 minus the velocity of 𝑏. Substituting in the values we are given, we have 25𝐢 is equal to 40𝐢 minus 𝐕 sub 𝑏. We can then add 𝐕 sub 𝑏 and subtract 25𝐢 from both sides of our equation. This gives us 𝐕 sub 𝑏 is equal to 40𝐢 minus 25𝐢, which is equal to 15𝐢.

The missing number is therefore equal to 15. If the velocity of 𝑎 relative to 𝑏 is 25𝐢 and the velocity of 𝑎 is 40𝐢, then the velocity of 𝑏 is 15𝐢. We can represent this on the one-dimensional coordinate axis as shown.