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?

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)

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

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°

To find the displacement from the starting point, we can represent the two distances and directions as vectors and then add them to get the resultant vector.

First, let's represent the first distance of 9km in the direction 246 degrees.

To convert the direction into Cartesian coordinates, we can use the following formulas:
x = cos(θ)
y = sin(θ)

So for 246 degrees:
x1 = cos(246 degrees)
y1 = sin(246 degrees)

Using a calculator or trigonometric tables, we can find that:
x1 ≈ -0.198
y1 ≈ -0.981

Therefore, the vector representing the first distance is:
V1 = 9 * (-0.198)i + 9 * (-0.981)j

Next, let's represent the second distance of 6km in the direction 096 degrees.

Using the same formulas:
x2 = cos(96 degrees)
y2 = sin(96 degrees)

Again, using a calculator or trigonometric tables, we find:
x2 ≈ 0.173
y2 ≈ 0.985

Therefore, the vector representing the second distance is:
V2 = 6 * (0.173)i + 6 * (0.985)j

Now, we can add these two vectors together to get the resultant vector:
R = V1 + V2

To add two vectors, we simply add their corresponding components:
Rx = V1x + V2x
Ry = V1y + V2y

So, substituting the values we found earlier:
Rx = (-0.198 * 9) + (0.173 * 6)
Ry = (-0.981 * 9) + (0.985 * 6)

Evaluating these equations:
Rx ≈ -2.040
Ry ≈ -0.309

Finally, the displacement from the starting point is given by the magnitude of the resultant vector:
displacement = √(Rx^2 + Ry^2)

Substituting the values:
displacement ≈ √((-2.040)^2 + (-0.309)^2)
displacement ≈ √(4.162 + 0.095)
displacement ≈ √4.257
displacement ≈ 2.064

Therefore, the displacement from the starting point is approximately 2.064 km.