Question

In its daily prowl of the neighborhood, a cat makes a displacement of 128m due north, followed by a 70m displacement due west.
a) Find the (a) magnitude and (b) direction of the displacement required for the cat to return home.
b) If, instead, the cat had first prowled 70m west and then 128m north, how would this affect the displacement needed to bring it home? Explain.

Answer 1

Given thatthe  initial displacement is A = 128 m north

                         thefinal displacement B = 70 m west

---------------------------------------------------------------------------

               

    as shown in the above figure  themagnitude of the resultant vector A+B is

                                          R = ( A²+B²)^1/2

                                              = 145.89 m

   then the angle makes with the westdirection is   ? = tan^-1( A /B)

                                                                               =61.33 degrees (south-east)

  (B) If, instead, the cat had first prowled 70 mwest and then 128 m north

          thenthe magnitude of the resultant is same as R but angle isdifferent

                                                        as   ? = tan^-1( 70m / 128m)

                                                                               =28.67 degrees (south-east)