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 $\frac{1}{10}$ 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.? components: (0.30,0.70), magnitude: 0.76 components: (0.30,0.70), magnitude: 76 components: (30,70), magnitude: 0.76 components: (30,70), magnitude: 76

Explanation:

Step1: Scale components

If the final - landfall vector is \((3,7)\) and the 6 - am vector is \(\frac{1}{10}\) of the total - distance vector, then we multiply each component of the land - fall vector by \(\frac{1}{10}\). So the components of the 6 - am vector are \((3\times\frac{1}{10},7\times\frac{1}{10})=(0.30,0.70)\).

Step2: Calculate magnitude

The magnitude of a two - dimensional vector \(\vec{v}=(x,y)\) is given by \(|\vec{v}|=\sqrt{x^{2}+y^{2}}\). For the vector \((0.30,0.70)\), we have \(|\vec{v}|=\sqrt{(0.30)^{2}+(0.70)^{2}}=\sqrt{0.09 + 0.49}=\sqrt{0.58}\approx0.76\).

Answer:

A. components: (0.30,0.70), magnitude: 0.76