Chapter 8, Problem 8STP

To determine

The resultant velocity of Amy’s.

Answer to Problem 8STP

  $y=12.3$

  $x=8.4°\text{ east of north}$

Explanation of Solution

Given:

North = 10 feet per second

East of north = 40 degrees.

Velocity = 2.8 feet.

Calculation:

The figure can be drawn as:

Let the magnitude of resultant = y.

Let the direction of resultant = x degrees east of north.

The unknown can be labeled as:

According to law of cosine:

  $\begin{array}{l}{a}^2=b^2+c^2-2bc\cos A\\ \text{Therefore,}\\ y=\sqrt{{10}^2+{2.8}^2-2\left(10\right)\left(2.8\right)\cos 140°}\\ y=\sqrt{150.6196}\\ y=12.3\\ and\\ \cos x=\frac{{10}^2+{\left(12.3\right)}^2-{\left(2.8\right)}^2}{2\left(10\right)\left(12.3\right)}\\ \cos x=0.989634\\ x\approx {\cos }^{-1}0.989634\\ x\approx 8.4°\end{array}$