Agolfer takes three putts to get the ball into the hole. the first putt displaces the ball 3.45 m north, the second 1.53 m southeast, and the third 0.877 m southwest. what are (a) the magnitude and (b) the angle between the direction of the displacement needed to get the ball into the hole in just one putt and the direction due east?

magnitude is 2.52 m  with 66.15° north east

Explanation:

given data

displace 1 = 3.45 m north = 3.45 j

displace 2 = 1.53 m southeast = 1.53 cos(315) i + sin(315) j

displace 3 = 0.877 m southwest  = 0.877 cos(225) i- sin(225) j

to find out

displacement and direction

solution

we consider here direction i as east and direction j as north

so here

displacement = displace 1 + displace 2 + displace 3

displacement =  3.45 j + 1.53 cos(315) i + sin(315) j + 0.877 cos(225) i- sin(225) j

displacement =  3.45 j + 1.081 i -1.0818 j - 0.062 i -0.062 j

displacement = 1.019 i + 2.306 j

so magnitude

magnitude =

magnitude = 2.52

and

angle will be = arctan(2.306/1.019)

angle = 1.15470651 rad

angle is 66.15 degree

so magnitude is 2.52 m  with 66.15° north east