Answer to Question #91700 in Classical Mechanics for Louie

Question

Question 14
A radar station at O tracks two ships P & Q. P has position vector (2i + 4j) km, and Q has position vector (7i + 6j) km. What is the magnitude of the distance between ships?

Answer 1

$$\vec P = 2\vec i + 4\vec j \equiv (2,4)$$ $$\vec Q = 7\vec i + 6\vec j \equiv (7,6)$$

$$\vec Q - \vec P = (7,6) - (2,4) = (7-2, 6-4) = (5,2)$$ $$d = |\vec Q| = \sqrt{5^2 + 2^2} = \sqrt{25+4} = \sqrt{29}$$