Question

The vector A= 90m/s towards north and vector B = 125 m/s towards west. Find the magnitude of the resultant vector using pythagorean theorem

Answer 1

154.03 m/s

Explanation

The Pythagorean theorem states that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)

$a^2+b^2=c^2$

so, to add the vectors we solve use tht P.T and solve for c

s

Step 1

a) let

$\begin{gathered} a=\text{ Vector A=90 }\frac{m}{s} \\ b=\text{ Vector B=125 }\frac{m}{s} \\ c=\text{ unknown= maginutude of the resultant} \end{gathered}$

b) now, replace in the formula:

$\begin{gathered} a^2+b^2=c^2 \\ 90^2+125^2=c^2 \\ 8100+15625=c^2 \\ 23725=c^2 \\ square\text{ root in both sides} \\ \sqrt{23,725}=\sqrt{c^2} \\ 154.03=c \end{gathered}$

therefore, the answer is

154.03 m/s

I hope this helps you