Question

You are given a vector in the xy plane that has a magnitude of 86.0 units and a y component of -55.0 units.

a.)What are the two possibilities for its x component?

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.

Answer 1

(a) The two possibilities for the x component is that either it can be +ve or -ve.
As we know that the magnitude of the vector is given by
A= (X² + Y²)^1/2
where A is the magnitude of the vector
X and Y are the components of the vector.
Now putting all the values
86² = [X² + (-55)²]
X² = 86² - (-55)²
X² = 4371
X = 66.11 units
(b) If x component is positive then the orignal vector will be
= 66.11 i - 55 j
Resultant vector
= 80 i + j
Now the vector which should be added to the to provide
So let us consider that the vector which we are adding is ,therefore
+ =
(66.11 i - 55 j ) + = (80 i + 0 j )
= (80 -66.11) i + ( 0 +55)j
= 13.89 i + 55 j
(c) Direction of the
tan = Y component / x component
tan = 55 /13.89
= tan^-1(55/13.89) = 75.83 in anticlockwise direction from + x direction