A golfer takes two putts to get his ball into the hole once he is on the green. The first putt displaces the ball 8.10 m east, the second 6.00 m south. What displacement would have been needed to get the ball into the hole on the first putt?
To find the displacement needed to get the ball into the hole on the first putt, we can use the Pythagorean theorem. The displacement can be found by calculating the length of the hypotenuse of a right triangle formed by the two displacements given.
Here's how you can calculate it step by step:
1. Draw a diagram to represent the displacement of the ball. Let's assume that east is the positive x-direction and south is the negative y-direction.
2. Label the first putt as displacement A, which is 8.10 m east. Label the second putt as displacement B, which is 6.00 m south.
3. Use the Pythagorean theorem, which states that the square of the hypotenuse is equal to the sum of the squares of the other two sides. In this case, the hypotenuse represents the displacement needed to get the ball into the hole on the first putt.
4. Calculate the square of the length of displacement A by squaring 8.10 m: 8.10^2 = 65.61 m^2.
5. Calculate the square of the length of displacement B by squaring 6.00 m: 6.00^2 = 36.00 m^2.
6. Add the squares of the two displacements together: 65.61 m^2 + 36.00 m^2 = 101.61 m^2.
7. Take the square root of the sum to find the length of the hypotenuse, which represents the displacement needed to get the ball into the hole on the first putt: √101.61 m^2 ≈ 10.08 m.
Therefore, the displacement needed to get the ball into the hole on the first putt is approximately 10.08 m.