Question

Question #703a5

Answer 1

The two parts of her journey are at right angles, so we just need the length of the hypotenuse from Pythagoras' law.

Explanation:

The square of the hypotenuse is equal to the sum of the squares of the other two sides.

`20^2 + 15^2` = 625 but we still need to find the square root

`sqrt`625 = 25 so she travels 25 miles as the crow flies, despite having covered 35 miles of driving.

The displacement is shorter than the distance traveled.

Answer 2

`25 "miles to south east"`

Explanation:

In your example, we are dealing with two vectors where we have to add them to find the resultant disposition vector.
Inserting the 2 vectors as seen in the image, a right triangle is formed, where the hypotenuse (the side opposite to right angle is the resultant vector).

The resultant vector will be calculated using the Pythagorean Theorem which states that:
`a^2= b^2+c^2`
where a= hypotenuse
b,c= other sides

Applying the theorem:
`diposition^2=20^2+15^2=400+225=625`
`disposition= sqrt(625)=25 "miles"`

`rarr "the resultant vector" = 25 "miles to south east"`