What must be the y component of this vector so that it's magnitude is 10.0 units?

Question

A vector in the xy-plane has an x component of -7.50 units. What must be the y component of this vector so that it's magnitude is 10.0 units?

Answer 1

Recall that the "magnitude" of a vector is just how long the vector is. That can be calculated with none other than the Pythagorean theorem. That formula looks like this.

 

|V| = √[(V_x)² + (V_y)²]

 

|V| stands for the magnitude of the vector. For this problem, I just called the vector, "V." Someone was nice enough to already give the x-component of the vector, which is -7.50 units. Plug this in for V_x. The magnitude also needs to be 10.0, so plug that in for |V|.

 

|V| = √[(V_x)² + (V_y)²]

10 = √[(-7.50)² + (V_y)²]

10 = √[56.25 + (V_y)²]

 

Solve for "V_y" to get the y-component. Solve for that first by squaring both sides.

 

10 = √[56.25 + (V_y)²]

100 = 56.25 + (V_y)²

43.75 = (V_y)²

V_y = √43.75 ≈ 6.61

 

I hope this helps, and good luck with the rest of your class!