Question

You are given a vector in the xy plane that has a magnitude of 86.0 units and a y component of -40.0 units. Assuming the x component is known to be positive, specify the vector V? which, if you add it to the original one, would give a resultant vector that is 70.0 units long and points entirely in the -x direction. only need answer...in vx,vy

Answer 1

86^2 = x^2 + (-40)^2

=> x^2 = 86^2 - 40^2 = 5796

=> x = +- sqrt(5796) = +/- 76.13

taking x = +76.13

new vector have coordinates (a,b)

a + 76.13 = -70

=> a = -146.13 units

and b + (-40) = 0

=> b = 40 units

new vector is (-146.13 , 40)

i.e vx = -146.13 and vy = 40

magnitude = (-146.13)^2 + (40)^2 = 151.51 units

angle = tan^-1 ( y component/ x component)

       = tan^-1 (40 / -146.13)

         = - 15.31 degrees or 164.7 degress