Calculate the magnitude of a vector with horizontal component = 100 and vertical component = 173.

Answer 1

Hi Emy!

This question can be solved by thinking of the horizontal and vertical components of the vector as horizontal and vertical side lengths of a right triangle. The magnitude of the vector is the same as the length of the hypotenuse of that triangle. This allows us to solve for the magnitude using the Pythagorean theorem:

a² + b² = c²

In this case, a is the horizontal component, b is the vertical component and c is the magnitude of the vector. Solving this equation for c:

c = (a² + b²)^1/2

and substituting the values:

c = (100² + 173²)^1/2

c = 199.8

Therefore, the magnitude of the vector is 199.8.

I hope this helps!