Question

A golfer takes two putts to sink his ball in the hole. The first putt displaces the ball 6.50 m east, and the second putt displaces it 5.90 m south. What displacement would put the ball in the hole in one putt?

Answer 1

Displacement to hole from initial position is 8.78 m at direction 42.23° south of east.

Explanation:

Let east represent X axis and north represent Y axis.

We need to find what displacement would put the ball in the hole in one putt.

The first putt displaces the ball 6.50 m east

First displacement = 6.50 i m

The second putt displaces it 5.90 m south

Second displacement = -5.90 j m

Total displacement = 6.50 i - 5.90 j

$\texttt{Magnitude = }\sqrt{6.50^2+(-5.90)^2}=8.78m\\\\\texttt{Direction = }tan^{-1}\left ( \frac{-5.9}{6.5}\right )=-42.23^0$

So displacement to hole from initial position is 8.78 m at direction 42.23° south of east.