A golfer takes two putts to get his ball into the hole once he is on the green. The first putt displaces the ball 6.90 m east, the second 7.70 m south. What displacement would have been needed to get the ball into the hole on the first putt?

Answer 1

V1 = (6.90m,0 deg).
V2 = (7.7m,270 deg).

X = hor. = 6.90cos(0) + 7.7cos270,
X = 6.90 + 0 = 6.90m.

Y = ver. = 6.90sin(0) + 7.7sin270,
Y = 0 + (-7.7) = -7.7m.

tanA = Y / X = -7.7 / 6.9 = -1.1159,
A = -48.1 deg,CW.
A = -48.1 + 360 = 312 deg.,CCW.

D = X / cosA = 6.90 / cos312 = 10.3m @
312 deg.