If Vx= 6.80 and Vy= -7.40 units, determine the magnitude and direction of V and an arrow pointing right ?

Question

The V has an arrow pointing right over it

Im confused, please explain

Answer 1

------->  |   Vx = 6.80V

           |

          V    

Vy = -7.4 (Vector diagram)

So, resultant magnitude would be: (pythagoras)

x^2 + y^2 = m^2

= 6.8^2 + 7.4^2 = m^2

= 101 (sqrt) = 10.05 units

And direction = angle between Vx and the hypotenuse... so we have adjacent and hypotenuse lengths (6.8 and 10.05), so we use cosine...

= direction = cos(6.8/10.05) = 0.999... inverse cos =

direction = 47.4 degrees

Answer 2

you would use the pythagorean theorem to find the magnitude of v

v^2 = Vy^2 + Vx^2

to find the direction of v you would use trigonometry

tan theta = Vy/ Vx

theta = tan^-1 (Vy/Vx)