Question

The Very Large Array in western New Mexico consists of several radio

telescopes that can be rearranged along railroad tracks. The largest of
these arrangements has the telescopes positioned in a “Y” pattern for
18 km along three separate tracks. Suppose an electrician inspects the
instruments in each antenna from the end of the northern track the
end of the southwestern track. If the electrician's resultant displace-
ment is 31.2 km at 30 0° west of south, what are the southern and west-
ern components of the displacement?

Answer 1

Explanation: The formula to calculate the magnitude of the displacement is

sqrt((x2 - x1)^2 + (y2 - y1)^2) where x1 and y1 are the coordinates of the first

point and x2 and y2 are the coordinates of the second point. Using this

formula, we can find the magnitude of the displacement between the two

points as follows:

sqrt((3657.36 - 0)^2 + (30.0)^2) = sqrt(10^6) km

The southern component of the displacement is given by the negative

value of the eastward component of the displacement since the direction

of movement is counterclockwise from north to south. Therefore, it is:

(sqrt(10^6) *