Question

Two tectonic plates, P and Q, move in opposite directions along a transform fault boundary. If the plate velocity of P is 8 cm/year and of Q is 6 cm/year with respect to a fixed reference frame, the relative velocity between P and Q is _______ cm/year (answer in integer).

Hint:

When two bodies move in opposite directions along the same line, their relative velocity is the sum of their individual speeds, not the difference.

Answer 1

Correct Answer: 14

Step 1: Understand the setup.
Plates \(P\) and \(Q\) sit on either side of a transform fault and move in opposite directions relative to a fixed reference frame. The speed of plate \(P\) is \(v_P = 8\) cm/year and the speed of plate \(Q\) is \(v_Q = 6\) cm/year.

Step 2: Set up a sign convention.
Take the direction of plate \(P\)'s motion as positive. Since plate \(Q\) moves in the opposite direction, its velocity is negative relative to the same axis,
\[ v_P = +8 \text{ cm/year}, \qquad v_Q = -6 \text{ cm/year} \]

Step 3: Compute the relative velocity.
The relative velocity between the two plates, that is how fast one plate moves with respect to the other, is the vector difference
\[ v_{rel} = v_P - v_Q = 8 - (-6) = 8 + 6 \]

Step 4: Evaluate.
\[ v_{rel} = 14 \text{ cm/year} \]
This makes physical sense, because when two plates move away from each other or towards each other along a fault, their individual speeds add up to give the total closing or slipping rate at the boundary.

Step 5: Final conclusion.
The relative velocity between plates \(P\) and \(Q\) along the transform fault is
\[ \boxed{14 \text{ cm/year}} \]