Question

A hurricane was detected in the Atlantic around 5 a.m. The National Weather Service determined that it will make landfall at a location described by a vector with components [3, 7]. Around 6 a.m. on the same path, the hurricane is 1/10 the total distance from where it was detected initially to where it will make landfall.

If the hurricane is traveling on a straight path, what are the characteristics of the vector representing the path of the hurricane at 6 a.m.?

A) components: [0.30, 0.70], magnitude: 0.76
B) components: [0.30, 0.70], magnitude: 76
C) components: [30,70], magnitude: 0.76
D) components: [30,70], magnitude: 76

Answer 1

The correct option is;

A) Components: [0.30, 0.70], magnitude: 0.76

Explanation:

The given parameters are;

The path of the of the airplane at 5 a.m. given by The National Weather Service = [3, 7]

The location of the hurricane at 6 a.m. = 1/10 of the total distance between the point where it was detected to the point where it is predicted to make land fall

Therefore;

The components of the vector at 6.00 a.m. = 1/10 × [3, 7] = [0.3, 0.7]

The magnitude of the vector at 6.00 a. m. = √(0.3² + 0.7²) ≈ 0.76.