Question

You are given a vector in the xy plane that has a magnitude of 87.0 units and a y component of -55.0 units.

a)

What are the two possibilities for its x component?

Enter your answers using three significant figures separated by a comma.

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

c)

Specify the direction of the vector.

Express your answer using three significant figures

Answer 1

Given

vector A in XY plane of magnitude is 87 units

with y component is y= -55 units

the x component of the given vector is  

a)

87 = sqrt( x^2+(-55)^2)

solving for x  

the possible values are x = +67.409 units and x = -67.409 units

b) now the resultant vector is in the -x direction so

if we add +x value of the vector A , to the resultant vector R be in the -ve x direction , so that the x component of the resultant vector soud be -ve

that is -80 = 67+x ==> x = -147 units as x component

c) the direction of the vector is along the - x direction , if the resultant vector is along x direction taht is the y comoponent is zero