Question

A boat’s velocity measured in meter per second, is described by vector b=<3,-4>. In two or more complete sentences explain how to find the speed of the boat and the direction it is traveling in standard position. In your final answer, include all of your calculations.

Answer 1

Answer:

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Step-by-step explanation:

Answer 2

Answer:

The term speed is used to denote distance  traveled divided by time. The speed is the magnitude of instantaneous  velocity and so can never be negative. In this problem, we have a boat’s velocity measured in meter per second, described by vector:

$b=(3,-4)$

1. Therefore, the magnitude of this vector, which is also the speed of the boat can be found as:

$\left|b\right|=\sqrt{3^2+(-4)^2}=5m/s$

2. On the other hand, the direction the boat is traveling is the angle that this vector makes with the horizontal. So this can be found as:

$\theta = tan^{-1}(\frac{3}{-4})=-36,86^{\circ}$

The representation of this problem is shown below.