Question

A golfer takes two putts to get his ball into the hole once he is on the green. The first putt displaces the ball 8.4 m east, and the second 4.33 m south. What displacement would have been needed to get the ball into the hole on the first putt?

Answer 1

The displacement needed to get the ball into the hole on the first putt is approximately 9.6 m.

Step-by-step explanation:

To find the displacement needed to get the ball into the hole on the first putt, we need to find the resultant displacement of the two putts. The first putt displaced the ball 8.4 m east, and the second putt displaced it 4.33 m south. To find the resultant displacement, we can use the Pythagorean theorem. The displacement needed to get the ball into the hole on the first putt is the hypotenuse of a right triangle with sides 8.4 m and 4.33 m. Using the Pythagorean theorem, we can calculate the displacement to be approximately 9.6 m.

Answer 2

d=9.45 m

And directed

α=62.7⁰

Step-by-step explanation:

The Pythagoras Theorem

"The theorem, also known as the Pythagorean theorem, states that the square of the length of the hypotenuse is equal to the sum of squares of the lengths of other two sides of the right-angled triangle"

so for this problem

`d^(2)=b^(2)+c^(2)\\   d=\sqrt{b^(2)+c^(2)}\\ d=\sqrt{(8.4)^(2)+(4.33)^(2)  }\\ d=9.45m`

And directed

α=tan⁻(8.4/4.33)

α=62.7⁰