Question #703a5

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Question #703a5

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Answer 1 · 2017-09-13T21:13:27

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.

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

$\sqrt{}$ $sqrt$ 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 · 2017-09-13T21:14:40

$25 miles to south east$ $25 "miles to south east"$

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:
$a^{2} = b^{2} + c^{2}$ $a^2= b^2+c^2$
where a= hypotenuse
b,c= other sides

Applying the theorem:
$d i p o s i t i o n^{2} = 20^{2} + 15^{2} = 400 + 225 = 625$ $diposition^2=20^2+15^2=400+225=625$
$d i s p o s i t i o n = \sqrt{625} = 25 miles$ $disposition= sqrt(625)=25 "miles"$

![https://www.mathsisfun.com/algebra/http://vector-calculator.html](https://useruploads.socratic.org/EnvgcjigTfu3a5m8QuAD_150533663206036.jpg)

$\to the resultant vector = 25 miles to south east$ $rarr "the resultant vector" = 25 "miles to south east"$

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Question #703a5

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