Question

A vector's x component is six times its y component. What is the acute angle between the vector and the +x axis?

Answer 1

Let the vector be Ai + Bj

anglfrom x axis is given by,

$\theta$ = otan^-1(B/A)

A and B are the x and y components respectively,

i and j are unit vectors in x and y directions respectively

given, A = 6*B

hence the angle is

$\theta$ = tan^-1(B/A) =  tan^-1(B/6B) =tan^-1(1/6)

$\theta$ = 9.462^o

Let the initial distance of Lil from the foot of the tower be 'L', and the height of the tower be 'h'

then for the initial triangle made

tan(18)= h/L

L = h/(tan(18))

when she moves a distance of x

tan(22.2) = h/(L-x)

L-x = h/tan(22.2)

putting the value of x and L

h/tan(18) - 891 = h/tan(22.2)

h*{1/tan(18) - 1/tan(22.2)} = 891

h = 1420.467 ft