A golfer takes two putts to get his ball into
the hole once he is on the green. The first putt
displaces the ball 9.6 m east, and the second
2.59 m south.
What displacement would have been
needed to get the ball into the hole on the
first putt?
Answer in units of m
Answer: 9.94 m
i have the answer to the first part i just don't get the second part which is,
What is the direction (in degrees S of E)?
Answer in units of ◦
D = 9.6-2.59i
D^2 = 9.6^2 + (-2.59)^2 = 98.89
D = 9.94 m.
tan A = Y/X = -2.59/9.6 = -.26979
A = -15.1o = 15.1o S of E.
A bicyclist makes a trip that consists of three parts, each in the same direction (due north) along a straight road. During the first part, she rides for 21.0 minutes at an average speed of 9.48 m/s. During the second part, she rides for 43.5 minutes at an average speed of 3.20 m/s. Finally, during the third part, she rides for 10.2 minutes at an average speed of 10.5 m/s. (a) How far has the bicyclist traveled during the entire trip? (b) What is the average speed of the bicyclist for the trip?
To determine the displacement needed to get the ball into the hole on the first putt, you can use vector addition. The first putt displaced the ball 9.6 m east and the second putt displaced it 2.59 m south.
To get the total displacement, you need to find the resultant vector of these two displacements. You can do this by calculating the magnitude and direction of the resultant vector.
1. Magnitude of the resultant vector:
The magnitude of the resultant vector can be found using the Pythagorean theorem. The magnitudes of the east and south displacements form the legs of a right triangle, where the resultant vector is the hypotenuse.
magnitude = sqrt((9.6^2) + (2.59^2))
2. Direction of the resultant vector:
The direction can be found using trigonometry. The east displacement creates an angle θ with the positive x-axis (east), and the south displacement creates an angle φ with the positive y-axis (north). The direction of the resultant vector can be calculated by finding the sum of these angles.
First, find the angle θ:
cos(θ) = adjacent/hypotenuse = 9.6 magnitude/resultant magnitude
θ = acos(9.6 magnitude/resultant magnitude)
Then, find the angle φ:
sin(φ) = opposite/hypotenuse = 2.59 magnitude/resultant magnitude
φ = asin(2.59 magnitude/resultant magnitude)
Finally, the direction of the resultant vector is the sum of θ and φ:
direction = 180° - (θ + φ)
Plugging the values into the formula:
θ = acos(9.6/√(9.6^2 + 2.59^2))
φ = asin(2.59/√(9.6^2 + 2.59^2))
direction = 180° - (θ + φ)
After calculating these values, you should get the answer for the direction in degrees south of east.