Question

Find the magnitude and direction for 101m,60.0,85.0m

Answer 1

Answer:

magnitude = 161.3m, ∅ = 32.9°

Explanation:

Vector addition always works the same. Add two vectors by adding their respective components.

vector A: $\left[\begin{array}{c}85.0&0.0\end{array}\right]$

vector B:$101.0\left[\begin{array}{c} cos60.0&sin 60.0\end{array}\right] =\left[\begin{array}{c}50.5&87.5\end{array}\right]$

Adding vector A and B: $\left[\begin{array}{c}85.0&0.0\end{array}\right] +\left[\begin{array}{c}50.5&87.5\end{array}\right] = \left[\begin{array}{c}135.5&87.5\end{array}\right]$

The magnitude of any vector $\left[\begin{array}{c}a&b\end{array}\right]$ is given by the Pythagorean theorem:

$magnitude = \sqrt{a^2+b^2}$

In the case of the vector A+B:

$magnitude = \sqrt{135.5^2+87.5^2}$

The angle ∅ of the vector can by found by using trigonometric functions:

For instance, the angle ∅ for a vector $\left[\begin{array}{c}a&b\end{array}\right]$ is given by the equation:

$tan\phi= \frac{b}{a}$

The direction ∅ can be found by solving the trigonometric function.

In the example of vector A+B:

$tan\phi = \frac{87.5}{135.5}$

Solving for ∅:

$\phi = tan^{-1} (\frac{87.5}{135.5})=32.9$