Adisplacement b of 100m from the origin at an angle of 37° above the x axis is the result of three successive displacement : b1 of 100 along the negative x axis, b2 of 200m at an angle of 150° above the x axis and a displacement b3. find b3[ 355m, 353.5]

(353.1 m, -39.8 m)

Explanation:

Let's start by writing the components of the resultant displacement, B:

We know that this displacement is the result of three successive displacements, which can be written in terms of their components, as follows:

and , whose components are unknown.

The components of the resultant displacement must be equal to the sum of the components of each vector along each direction, therefore:

and

So, the vector b3 has components (353.1 m, -39.8 m).

see the picture for the vector

the magnitude of the vector by pythagorean theorem

r = √( (-10)^2 + (3)^2 ) = √109

magnitude = √109 units

the direction angle between vector and x-axis is

tan^(-1)(3/10) = 16.699

so the direction is approximately 16.7 degrees north of west