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.