You are given a vector in the xy plane that has a magnitude of 81.0 units and a

Question

You are given a vector in the xy plane that has a magnitude of 81.0 units and a y component of -56.0 units. What are the two possibilities for its z component? Enter your answers using three significant figures separated fry a comma. Assuring the z component is known to be positive, specify the magnitude of the vector which, if you add it to the original one, would give resultant vector that is 80.0 units long and points entirely in the -x direction. Scotty the direction of the vector. Express your answer using three significant figures.

Explanation / Answer

Part A ) given Vector magnitude = 81.0 units

and y- component =-56.0

x-component = square root(81.02 - (-56.0)2)

= +,- 58.52

so possibility for x-components are

x1,x2 = +58.2 ,-58.2 (units)

Part B) x-component of 81.0 magnitude vector =+58.2 units

the new resultant vector pointing entirely in -x direction means there is no y component

so, x-component of resultant vector =-80.0 units

y-component of resultant vector = 0

consider the vecor which is added to the vector of magnitude 81.0 is V and having x and y components as Vx and Vy respectively

so,

x-component of Resultant vector= x-component of 81.0 magnitude vector + Vx

-80.0= 58.2 +Vx

Vx=-80.0-58.2

Vx= -138.2 units

similarly,

y-component of Resultant vector= y-component of 81.0 magnitude vector + Vy

0 = -56.0 + Vy

Vy= +56.0 units

the magnitude of vector V =square root( Vx2 +Vy2 )

V= square root( (-138.2)2+56.02)

V =149.12 units

Part C) direction of vector V= arctan(Vy/Vx)

=arctan(56.0/(-138.2))

=-22.01 degrees

so the vector V is in 2nd Quadrant

direction=180.0-22.01=157.98 degrees with +x axis in anticlockwise direction

or direction =N 67.99 deg W

  

  

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