Download Golf Range Physics: Projectile Motion and Trajectory Analysis and more Exams Nursing in PDF only on Docsity!
At very high angle because that means the ball will go a lot farther with
the angle you hit it
The ball is heavier than major league home runs because the ball has
a smaller surface ear and there is not much wind resistance
The ball did not go far enough
What were the velocity and launch angle values? Name: Steve Peralta Date: 10-2-
Student Exploration:
Golf Range
Directions: Follow the instructions to go through the simulation. Respond to the questions and prompts in the orange boxes. Vocabulary: acceleration, air resistance, gravity, hang time, launch angle, projectile motion, trajectory, vector, velocity Prior Knowledge Questions (Do these BEFORE using the Gizmo.)
- You are in a contest with your friends to see who can drive a golf ball the farthest. Should you hit a “line drive” (low to the ground) or a shot with a very high angle? Explain.
- Golf drives travel much farther than Major League home runs. Why might this be? Gizmo Warm-up Have you ever hit a hole-in-one? You will have a chance to do that in the Golf Range Gizmo, where you will see how a variety of factors affect the path of a golf ball. The movement of objects such as a ball through space is called projectile motion.
- Press Play ( ). Did the ball go too far, the right distance, or not far enough?
- Click Reset ( ). Move the vinitial and θ sliders to adjust the velocity and launch angle until you get a hole-in-one. (With the Gizmo sound on ( ) you will hear “Hole in one!”)
100 m/s and 72 Degrees. 64 m/s and 43 degrees.
- Can you get holes-in-one using other combinations of vinitial and θ? If so, give an example. Reproduction for educational use only. Public sharing or posting prohibited. © 2020 ExploreLearning™ All rights reserved
Reproduction for educational use only. Public sharing or posting prohibited. © 2020 ExploreLearning™ All Activity B: Get^ the^ Gizmo^ ready: Physics of projectile motion ● Click Clear paths and select Atmosphere: None. ● Turn off Show grid and Show paths. ● You will need a scientific calculator for this activity. Introduction: Velocity is an example of a vector quantity because it describes the speed and direction of an object. The velocity of an object through space can be shown by two components: a horizontal component ( vx ) and a vertical component ( vy ). Question: How does the velocity of an object change as it flies through space?
- Observe Click Reset. Turn on Show velocity vector and Show velocity components. Set vinitial to 50 m/s and set θ to 45.0 degrees. Click Play. Focus on the blue and red arrows that represent the vertical and horizontal components of the golf ball’s velocity. A. As the ball flies through the air, what do you notice about the blue (vertical) arrow?
The blue barrow was not present
at the top of the parabola and
gravity was only affect on the way
down
B. As the ball flies through the air, what do you notice about the red (horizontal) arrow?
the red arrow does not change
at all because it is in a
horizontal motion
C. Try other velocities and launch angles. Do these results hold up? Yes they do
- Calculate: You can use trigonometry to find the initial horizontal and vertical components of the ball’s velocity. Take out your calculator now. Click Reset , and turn off Show velocity vector and Show velocity components. Set vinitial to 50.0 m/s and θ to 60.0 degrees. A. (^) To calculate vx , multiply vinitial by the cosine of the angle: v x = vinitial • cos( θ ): 25 m/s B. (^) To calculate v y , multiply vinitial by the sine of the angle: v y = vinitial • sin( θ ): 43.30 m/s
C. Turn on Show velocity components. Were you correct? yes
- Analyze: An object flying through the air is said to be in free fall. As you observed, the horizontal component of velocity ( v x ) does not change as the object moves, but the vertical component ( v y ) decreases over time. (Note: Air resistance is not included in this model.)
Reproduction for educational use only. Public sharing or posting prohibited. © 2020 ExploreLearning™ All A. (^) What force causes v y to change as the golf ball travels?
The mass of the golf ball
Reproduction for educational use only. Public sharing or posting prohibited. © 2020 ExploreLearning™ All
field
The velocity multiply by the time it took will give you the distance while assuming no air
resistance
What is the initial value of v y? Were your calculations correct? Reproduction for educational use only. Public sharing or posting prohibited. © 2020 ExploreLearning™ All Activity C: Hangtime Get the Gizmo ready: ● Set vinitial to 75 m/s, θ to 50.0 degrees, and g to 9.8 m/s^2. (Be sure Advanced features is on.) ● Check that Atmosphere: None is selected. Question: How can you calculate the distance a golf ball travels?
- Think about it: Suppose you know a golf ball’s horizontal velocity ( vx ) and the time it had traveled through the air ( t ). How could you calculate how far the ball traveled?
- Observe:
- Calculate: The vertical velocity of a projectile is found with the equation: v y = v y(initial) – gt. A. What will be the value of vy when the ball is at the top of its trajectory? 0m/s B. (^) Using the equation above, solve for t when v y = 0.0 m/s,^ v y(initial) = 57.45 m/s, and g = 9.81 m/s^2 5.8 s C. Now use the same method to determine how long it will take the ball to fall from its maximum height to the ground: 5.8s D. Based on your answers to B and C, how long will the ball spend in the air? 11.7 s This is the hang time of the ball.
- Check: Now press Play and observe the total time the ball spends in the air.
- Evaluate Click Reset. If the ball has a horizontal velocity ( vx ) and a hang time ( t ), you can find the horizontal distance the ball travels using d = vx • t (distance = velocity × time).
A. What is the horizontal velocity of the golf ball? 48.21m/s
B. What is the hang time of the ball? 11.7s
C. How far will the ball travel before it hits the 564m
yes
57.45m/s
Were your calculations correct? vx 38.3 m/s vy Reproduction for educational use only. Public sharing or posting prohibited. © 2020 ExploreLearning™ All D. Turn on Show grid and click Play. About how far did the ball travel?
564m
- Calculate Click Reset. Set vinitial to 50 m/s and θ to 40 degrees. Use what you have learned to calculate vx , vy , the hang time of the ball, and the horizontal distance the ball will travel. 32.14 m/s Hangtime 6.5 Distance 6.5 s
- Test: Check your answers using the Gizmo.
- Apply: Complete the following table, first calculating the answers and then verifying them with the Gizmo. Include all units. v initial θ v x (m/s) v y(initial) (m/s) Hang^ time^ (s)^ Distance (m) 60 m/s
52 m/s 30 m/s 6.1 s 315 m 30 m/s
21.21m/ s 21.27 m/s 4.33 s 90 m 80 m/s
40 m/s 69.3 m/s 14.15 s 565 m 50 m/s
12.94 m/s 48.38 m/s 9/87 s 127 m
- Challenge yourself: A classic problem in projectile motion is how far a projectile will travel if launched from a cliff. To solve this problem, you need to use the free-fall equation: h = gt^2 /2. Click Reset. Check that the selected atmosphere is None. With the Advanced feature’s checkbox turned on, set the height of the person ( hperson ) to 200.0 m. Set vinitial to 50.0 m/s, θ to 0.0 degrees, and g to 9.8 m/s^2. A. (^) Solve the free-fall equation ( h = gt^2 /2) for t. 31.30 s B. Calculate the time it will take the ball to fall to the ground from a height of 200 meters and acceleration ( g ) of 9.81 m/s^2
6.39s
C. Based on the time and the horizontal velocity, how far will the ball travel horizontally? 319.5 m D. Press Play. What were the actual hang time and distance? 6.39 s and 319.5 m 10.Advanced challenge: Click Reset. Change θ to 30°. Calculate the hang time and distance traveled. (Hint: Use v y = v y(initial)
- gt for the time to apex, h = hinitial yes
Reproduction for educational use only. Public sharing or posting prohibited. © 2020 ExploreLearning™ All
- gt^2 /2 for the^ height of the apex, and h = gt^2 /2 for the time from apex to ground.) Predicted hang time: 4.7s Predicted distance traveled: 343 m Check your answers:
