The only part I get is the 2km [NE]. When it says to go 120° towards the right for the 1.5 km vector, I don't know how to manage that exactly or how to connect it to the 2km vector.
Any help would be GREATLY appreciated!
Thanks in advance!
The only part I get is the 2km [NE]. When it says to go 120° towards the right for the 1.5 km vector, I don't know how to manage that exactly or how to connect it to the 2km vector.
Any help would be GREATLY appreciated!
Thanks in advance!
Use a coordinate system with the x-axis pointing East and the y-axis pointing North. Then the direction NE is described by the vector $\displaystyle \vec v = (1,1)$.
Make a sketch.
You are dealing with a triangle where you know the length of two adjacent sides and the included angle.
2nd part.
I assume that you are asked to use vectors. According to my previous post the first part of the trip is described by a vector which has the direction (1, 1). This vector should have the length of 2. Therefore the first part is represented by the vector:
$\displaystyle \vec v = \left(\sqrt{2}\ ,\sqrt{2}\right)$
The second part of the trip is described by a vector which points at an angle of -75° to the East direction (=positive x-axis). Therefore the second vector is
$\displaystyle \vec u = 1.5\cdot (\cos(-75^\circ)\ ,\ \sin(-75^\circ)) = (0.388229\ ,\ -1.44889)$
The endpoint of the trip is detremined by the vector
$\displaystyle \vec e = (\sqrt{2}+0.38829\ ,\ \sqrt{2}+(-1.44889)) = (1.80244\ ,\ -0.03468)$
The distance between start point and endpoint is nothing but the length of $\displaystyle \vec e$
$\displaystyle |\vec e|\approx 1.80277$
Use the coordinates of $\displaystyle \vec e$ to calculate the direction.