# Question Video: Identifying the Relative Velocity in Relation to a Stationary Object Mathematics

A submarine fires a torpedo at a target as part of a training exercise. The velocity of the submarine relative to the stationary target is represented by the vector 𝐮. The velocity of the torpedo relative to the submarine is represented by the vector 𝐯. What does the vector 𝐮 + 𝐯 represent? [A] the speed of the torpedo [B] the speed of the submarine [C] the total distance the torpedo travels [D] the velocity of the submarine relative to the torpedo [E] the velocity of the torpedo relative to the stationary target

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### Video Transcript

A submarine fires a torpedo at a target as part of a training exercise. The velocity of the submarine relative to the stationary target is represented by the vector 𝐮. The velocity of the torpedo relative to the submarine is represented by the vector 𝐯. What does the vector 𝐮 plus 𝐯 represent? Is it (A) the speed of the torpedo? (B) The speed of the submarine. (C) The total distance the torpedo travels. (D) The velocity of the submarine relative to the torpedo. Or (E) the velocity of the torpedo relative to the stationary target.

Let’s begin by sketching a diagram of the situation. We are told that a submarine fires a torpedo at a stationary target. We are told that the velocity of the submarine relative to the stationary target is represented by the vector 𝐮. This can be written as 𝐕 sub s is equal to 𝐮. We are also given the relative velocity of the torpedo to the submarine. This velocity is equal to vector 𝐯.

When dealing with relative velocity, we know the velocity of 𝐴 relative to 𝐵 is equal to the velocity of 𝐴 minus the velocity of 𝐵 for any two bodies 𝐴 and 𝐵 moving along the same one-dimensional axis. This means that, in our question, the velocity of the torpedo relative to the submarine is equal to the velocity of the torpedo minus the velocity of the submarine, where these two velocities are relative to a stationary point, in this case the target.

Substituting in vector 𝐮 and vector 𝐯 from this question, we have 𝐯 is equal to 𝐕 sub T minus 𝐮. We can then add 𝐮 to both sides of this equation such that the velocity of the torpedo relative to the stationary target is 𝐮 plus 𝐯. This corresponds to option (E). The vector 𝐮 plus 𝐯 represents the velocity of the torpedo relative to the stationary target.