Question

A person drives north 6 blocks, then drives west 6 blocks. the displacement is a straight line from the starting point to the finish in a _____ direction

Answer 1

Displacement is a straight line from the starting point to the finish point
`6√(2)` blocks in North-West direction.

Explanation:

The figure below shows the movement of person and standard direction taken.

AB represents the movement of person 6 blocks towards north and BC represents the movement of person 6 blocks towards west. A to C defines the distance traveled by the person.

Displacement is defined as the shortest distance covered between two points.

Here, displacement is the distance between point A and C.

Since, angle at B is right angle So, ΔABC is a right angled triangle.

Pythagoras theorem states that in a right angled triangle sum of square of base and perpendicular is equal to the square of hypotenuse.

Applying Pythagoras theorem in ΔABC, we get

`(AC)^2=(AB)^2+(BC)^2`

`(AC)^2=(6)^2+(6)^2`

`(AC)^2=36+36`

`AC=√(72)`

`AC=6√(2)`

Thus, displacement is a straight line from the starting point to the finish point
`6√(2)` blocks in North-West direction.

Answer 2

For the answer to the question above, A person drives north 6 blocks, then drives west 6 blocks. the displacement is a straight line from the starting point to the finish in 8.49 blocks in a Northwest direction.
The Solution:
A^2+B^2=C^2

6*6+6*6 = sqrt(72)