John walks 15 paces north, then 12 paces east, followed by 3 paces south. draw the vector for John's movements and find the resultant vector. show your steps.
this is the only Information I got from my teacher so don't ask me for more info
well, apparently you have been taught something about vectors. They have both length and direction. I assume you know the compass directions.
Draw the three vectors given, starting each where the previous one ends.
The resultant is a vector which starts where the first one started, and ends where the last one ended.
To visualize this, get out some graph paper. Pick a starting point, and move your finger in the indicated directions, for the given number of squares. Draw lines where your finger moved. Those are the vectors.
north 15 - 3 = 12
east 12
Draw it like oobleck said !
the answers at the back of says 17 paces NE
so what is 12 times the square root of two
sqrt (12^2 + 12^2) = 12 sqrt 2 the hypotenuse of that triangle you drew.
I got 16.97
To draw the vector representing John's movements, we can use a coordinate grid. Let's assume that John starts at the origin (0,0).
1. Start by drawing an arrow from the origin pointing north. Label this arrow as '15' since John walks 15 paces north.
2. From the endpoint of the previous arrow, draw another arrow pointing east. Label this arrow as '12' since John walks 12 paces east.
3. From the endpoint of the previous arrow, draw another arrow pointing south. Label this arrow as '3' since John walks 3 paces south.
Now, let's find the resultant vector, which represents John's final displacement. We can find the resultant vector by calculating the sum of the individual vectors.
1. Start by adding the horizontal components (east and west) separately. The east component is +12 since John moved east, and there is no west component as he did not move west.
2. Next, add the vertical components (north and south) separately. The north component is +15, and the south component is -3 since John moved south.
3. So, the resultant vector in terms of components is (12, 15 - 3) or (12, 12).
4. Lastly, draw an arrow originating from the origin (0,0) with a length of 12 units and an eastward direction. This is the resultant vector.
Please note that the resultant vector's magnitude and direction may vary depending on the scale and orientation of the coordinate grid you use.