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

#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.

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/vector-calculator.html

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

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