Question

Find R and 0 given the components Rx =7.805 and Ry= 3.196

Answer 1

For this problem, we are given the two components of a certain vector. We need to determine the magnitude and angle of this vector.

Let's draw the situation to better understand the problem:

We can create a right triangle with the two components and the vector. We can determine the value of R by using Pythagora's theorem:

$\begin{gathered} R^2=(7.805)^2+(-3.196)^2\\ \\ R^2=60.9198+10.2144\\ \\ R^2=71.1342\\ \\ R=\sqrt{71.1342}=8.434 \end{gathered}$

The value of R is 8.434.

Now we need to determine theta, for that, we can use the sine relation, as shown below:

$\begin{gathered} \sin(\theta)=\frac{R_y}{R}\\ \\ \sin(\theta)=\frac{-3.196}{8.434}=-0.3789\\ \\ \theta=\arcsin(-0.3789)=-22.27º \end{gathered}$

The value of the angle is equal to -22.27º