You are given a vector in the x y plane that has a magnitude of 83.0 units and a

Question

You are given a vector in the xy plane that has a magnitude of 83.0 units and a y component of-63.0 units.

A) What are the two possibilities for its

x component?  = +/- 54.0

B) Assuming the

x component is known to be positive, specify the magnitude of the vector which, if you add it to the original one, would give a resultant vector that is 80.0 units long and points entirely in the ?x direction.

I got part A I just do not undestand how to get part B. I don't just want the answer, I want the process that you took to get that answer.

Thank you

Explanation / Answer

83^2 = x^2 + (-63)^2

=> x^2 = 83^2 - 63^2 = 2920

=> x = +- sqrt(2920) = +- 54.03

taking x = +54.03

new vector have coordinates (a,b)

a + 54.03 = -80

=> a = -134.03 units

and b + (-63) = 0

=> b = 63 units

new vector is (-134.03 , 63)

magnitude = (-134.03)^2 + (63)^2 = 148.07 units

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