Question

An adventurous dog strays from home, runs three blocks east, two blocks north, one block east, one block north, and two blocks west. Assuming that each block is about 100 m, how far from home and in what direction is the dog? Use a graphical method.

Answer 1

Answer:

Distance = 360.55 m

Direction = North-East

Step-by-step explanation:

In the question,

The adventurous dog starts from O, say.

He moves 3 blocks East = 300 m

then,

2 blocks North = 200 m

1 block East = 100 m

1 block North = 100 m

2 blocks West = 200 m

So,

Distance of the Dog's final position from the initial position.

OE is given by,

In triangle OLE, using Pythagoras theorem,

$OE^{2}=OL^{2}+LE^{2}\\OE^{2}=(200)^{2}+(300)^{2}\\OE^{2}=40000+90000\\OE=360.55\,m$

Therefore, the distance of Dog from the Home is 360.55 m and the direction of Dog from Home is North-East.

Answer 2

Answer:

360.55m

North East

The person above me is correct.

Because all the turns created are 90 degrees, you can simply add the values of the vectors.

<3,0>

<0,2>

<1,0>

<0,1>

<-2,0>

Once you add the vectors you will get,

<2,3>.

If you graph this vector, you will note it's between North and East. Which means the direction is NE.

To get the magnitude you put it into pythagorean.

sqrt(2^2 + 3^2) = 3.6055

To get it into meters, we multiply it by 100.

3.6055(100) = 360.55m