A dog searching for a bone walks 3.50m south, then 8.20m at angle 30.0o north of east and
finally 15m west. Using Graphical techniques, find the resultant displacement of dog.
Well you will have to draw the vectors. I can only do trig here.
North = -3.50 + 8.20 sin 30 = -3.5 + 4.1
East = 8.20 cos 30 - 15 = 8.2 * 0.866 - 15
magnitude = sqrt (North^2+East^2)
angle North of East = sin^-1 (North/East)
Watch out what quadrant you are in. (Quad II)
D = -3.5i + 8.2*cos30+(8.2*sin30)i - 15
D = -3.5i+7.1+4.1i-15 = -7.9+0.6i
D = 7.92 m[-4.34o] = 7.92m[4.34o] W. of N.
(-7.9i+0.6j)m
20
To find the resultant displacement of the dog, we need to add up all the individual displacement vectors. Let's break down the information given into vector components:
1. The dog walks 3.50m south. This can be represented as a displacement vector pointing downward with a length of 3.50m.
2. The dog then walks 8.20m at an angle of 30.0° north of east. To find the vector components of this displacement, we need to determine its horizontal and vertical components. The horizontal component can be found by multiplying the magnitude (8.20m) by the cosine of the angle (30.0°). The vertical component can be found by multiplying the magnitude (8.20m) by the sine of the angle (30.0°).
Horizontal component = 8.20m * cos(30.0°)
Vertical component = 8.20m * sin(30.0°)
3. Finally, the dog walks 15m west. This can be represented as a displacement vector pointing to the left with a length of 15m.
Now, let's plot these vectors on a graph:
1. Start by drawing a coordinate system with x and y axes.
2. Draw the first displacement vector pointing downward with a length of 3.50m. Label it as vector A.
3. Draw the second displacement vector with its horizontal and vertical components. The horizontal component should go to the right by the calculated value, and the vertical component should go upward by the calculated value. Label it as vector B.
4. Draw the third displacement vector pointing to the left with a length of 15m. Label it as vector C.
5. To find the resultant displacement, draw a vector from the starting point (origin) to the end point formed by the tip of the last vector. This represents the sum of the individual displacement vectors.
6. Measure the length and direction of the resultant vector using a ruler and a protractor, respectively. The length represents the magnitude of the resultant displacement, and the direction represents the angle it makes with the positive x-axis.
That's it! You have now found the resultant displacement of the dog using graphical techniques.