Question #703a5

2 Answers
Mark C.
Sep 13, 2017

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

sqrt625 = 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.

Taha Z.
Sep 13, 2017

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"

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

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

Related questions
Impact of this question
954 views around the world
You can reuse this answer
Creative Commons License