A golfer takes 2 putts to get his ball into the first hole once he is on the green. The first putt displaces the ball 8.9 m east, and the second 8.32 m south. What displacement woud have been needed to get the ball into the hole on the first putt? Answer in m
What is the direction ( in degrees south of east)? answer in degrees
d1=8.9m @ 0 deg., d2=8.32m @ 270 deg.
X=8.9m + 8.32cos270 = 8.9 + 0 = 8.9m.
Y = 8.9sin270 = -8.32m.
a. D = sqrt((8.9)^2 + (-8.32)^2)) = 12.2m Displacement.
b. tanA = -8.32 / 8.9 = - 0.9348.
A=-43.1 deg = 43.1 deg. South of East.
Thank you tremendously for your help!
To find the displacement needed to get the ball into the hole on the first putt, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse (longest side) is equal to the sum of the squares of the other two sides.
In this case, the two sides of the triangle are the displacements of the first putt (8.9 m east) and the second putt (8.32 m south), and we want to find the length of the hypotenuse (displacement needed for the first putt). Let's call this unknown displacement "x."
Using the Pythagorean theorem, we can set up the following equation:
x^2 = (8.9^2) + (8.32^2)
Calculating the values:
x^2 = 79.21 + 69.5424
x^2 = 148.7524
Taking the square root of both sides to solve for x:
x = sqrt(148.7524)
x ≈ 12.198 m
Therefore, the displacement needed to get the ball into the hole on the first putt is approximately 12.198 m.
To find the direction in degrees south of east, we can use trigonometry. We have a right-angled triangle with sides representing the displacements.
Using the tangent function, the angle θ (in degrees) can be calculated:
tan(θ) = opposite/adjacent
tan(θ) = 8.32/8.9
Calculating the value:
θ = tan^(-1)(8.32/8.9)
θ ≈ 43.7 degrees
Therefore, the direction of the displacement needed for the first putt is approximately 43.7 degrees south of east.
To find the displacement that would have been needed to get the ball into the hole on the first putt, we can use the Pythagorean theorem. The displacement is the straight-line distance between the starting point and the destination.
First, we square the distance traveled east and the distance traveled south:
(8.9 m)^2 = 79.21 m^2
(8.32 m)^2 = 69.2224 m^2
Next, we sum these squared distances:
79.21 m^2 + 69.2224 m^2 = 148.4324 m^2
Finally, to find the displacement, we take the square root of the sum:
√(148.4324 m^2) = 12.1767 m
Therefore, the displacement that would have been needed to get the ball into the hole on the first putt is approximately 12.18 meters.
To find the direction in degrees south of east, we can use trigonometry. We have the side lengths of a right-angle triangle (east and south distances), and we want to find one of the angles.
Using the tangent function, we can find the angle:
tan(θ) = opposite/adjacent
tan(θ) = (8.32 m)/(8.9 m)
Now, we can take the arctan of both sides to find the value of θ:
θ = arctan((8.32 m)/(8.9 m))
Using a scientific calculator, we find that θ ≈ 42.3717 degrees.
Therefore, the direction is approximately 42.37 degrees south of east.