If 𝐕 sub 𝑎𝑏 is equal to 20𝐢 and 𝐕 sub 𝑎 equals 45𝐢, 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 need to calculate the velocity vector 𝑏.
We recall that the velocity of 𝑎 relative to 𝑏 is the velocity of 𝑎 minus the velocity of 𝑏 for two bodies 𝑎 and 𝑏 moving along the same one-dimensional axis. Substituting in the values we are given, we have 20𝐢 is equal to 45𝐢 minus the velocity of 𝑏. By adding the velocity of 𝑏 and subtracting 20𝐢 from both sides of our equation, we have the velocity of 𝑏 is equal to 45𝐢 minus 20𝐢. This is equal to 25𝐢. The missing number in the question is 25.