Question

A mouse is trapped in a maze to find his way out he walks 15 miles east, makes a 90° left turn, walks 8 miles, makes another 90° left turn, and walks 10 miles. what is the magnitude of the resultant vector?

Answer 1

Step-by-step explanation:

Given;

We are given the directions taken by a mouse trapped in a maze.

To find its way out, it takes;

(a) 15 miles east

(b) Makes a 90 degree left turn

(c) Walks 8 miles

(d) Makes another 90 degree left turn

(e) Walks another 10 miles

Required;

We are required to find the magnitude of the resultant vector.

Step-by-step solution;

To do this, let us represent the movements from (a) to (e) on a diagram. This is shown below;

From the diagram above, we can see that the magnitude is the distance from the endpoint to the starting point and that has resulted in a side length that can be solved using the Pythagoras' theorem, as shown below;

Pythagoras' Theorem:

`\begin{gathered} Theorem: \\ c^2=a^2+b^2 \end{gathered}`

Where the variables are;

`\begin{gathered} c=hypotenuse \\ a,b=other\text{ }sides \end{gathered}`

We can now substitute the values given and solve as follows;

`c^2=5^2+8^2`
`c^2=25+64`
`c^2=89`

Take the square root of both sides;

`√(c^2)=√(89)`
`c=9.4339`

Rounded to 2 decimal places, the magnitude of the resultant vector is;

ANSWER:

`Magnitude=9.43\text{ }miles`