Question

a cargo ship left port a and is headed across the ocean to shipping port b. after one month, the ship stopped at a refueling station along a path described by a vector with components ⟨14,23⟩. after another month, on the same path, the ship reached port b, twice the distance from port a as the fueling station. what are the characteristics of the vector representing the path of the ship? components: (7,11.5), magnitude: 13.46 components: (7,11.5), magnitude: 53.85 components: ⟨28,46⟩, magnitude: 13.46 components: ⟨28,46⟩, magnitude: 53.85

Explanation:

Step1: Find the components of the vector

Since the ship reached port B, twice the distance from port A as the fueling station. If the vector of the fueling station is \(\langle14,23
angle\), then the vector of port B (path from A to B) is \(2\times\langle14,23
angle=\langle28,46
angle\) (scalar - vector multiplication).

Step2: Calculate the magnitude of the vector

The magnitude of a vector \(\vec{v}=\langle x,y
angle\) is given by \(|\vec{v}|=\sqrt{x^{2}+y^{2}}\). For \(\vec{v}=\langle28,46
angle\), \(|\vec{v}|=\sqrt{28^{2}+46^{2}}=\sqrt{784 + 2116}=\sqrt{2900}\approx53.85\)

Answer:

components: \(\langle28,46
angle\), magnitude: \(53.85\) (the fourth option)