Question

A man walk 9km in the direction 246 degrees and then for 6km in the direction 096 degrees...... What is the displacement from the starting point?..... Formula and answer please?

Answer 1

convert each displacement to rectangular form, and then just add them up.

Then if the final position is (x,y), the displacement is

√(x^2+y^2)

Answer 2

Can you the full working out for this question above...

Answer 3

Here's one example, along the same lines:

A man walk 7km in the direction 270 degrees and then for 9km in the direction 030 degrees.

Compass directions are clockwise from the north, so 270° compass = 90-270=-180 in the Cartesian plane.
Similarly, 030° compass = 90-30=60° in the Cartesian plane.

A. conversion to rectangular form:
distance X Y
7 km 7cos(-180) 7sin(180)
9 km 9cos(60) 9sin(60)
sum -7+4.5=-2.5 0+7.794=7.794
Displacement
=√(-2.5^2+7.794^2)
=√67
=8.185 (distance from origin)

Direction:
Since x is negative and y is positive, it is in the second quadrant. The reference angle is
A=atan(2.5/7.794)
=17.784°
and the actual angle from the positive x-axis is
theta=180-17.784
=162.22°

Finally, convert back to compass notation,
Angle=90-theta
=90-162.22
=-72.22
=360-72.22 (add 360 to convert to positive bearing)
=287.78°

The final answer would be

8.185km along the bearing 287.78°