Question

An object experiences two velocity vectors in its environment.v1 = −50i + 4jv2 = 5i + 15jWhat is the true speed and direction of the object? Round the speed to the thousandths place and the direction to the nearest degree.

Answer 1

First, let's add the vectors:

`v=v_1+v_2=(-50i+4j)+(5i+15j)=-45i+19j`

The true speed is given by the magnitude of the resulting vector:

`|v|=√((-45)^2+(19)^2)=√(2025+361)=√(2386)=48.847`

The direction can be calculated with the formula below:

`\begin{gathered} \theta=\tan^(-1)((19)/(-45))\\ \\ \theta=157° \end{gathered}`

Therefore the correct option is the first one.