Exam (elaborations) GIZMOS Student Exploration Feed the Monkey (Projectile Motion)

Exam (elaborations) GIZMOS Student Exploration Feed the Monkey (Projectile Motion) Prior Knowledge Questions (Do these BEFORE using the Gizmo.) Eccentric billionaire Veda Hussert has invented a “banana cannon” to help feed the monkeys on her personal wildlife preserve. To feed a monkey high in the trees, simply aim the cannon at the monkey and fire a banana! Unfortunately, the noise of the cannon frightens the monkeys, and they drop out of the tree when they hear the sound. 1. To hit a falling monkey with a banana, where should Veda aim? (Circle your choice.) A. Above the monkey B. Below the monkey C. Directly at the monkey 2. Explain your choice: Veda should aim the cannon at the monkey because both the monkey and the banana will undergo the same downward movement, such that the banana will be pulled down from its target at the same distance as it was aimed away from the monkey. Gizmo Warm-up The Feed the Monkey Gizmo shows a banana cannon and a monkey. When the cannon fires, the startled monkey drops from the branch. 1. Click Play ( ) to fire the cannon. What happens? The banana flies over top of the monkey’s head. 2. You can use the sliders to change the banana velocity (vInitial) and cannon angle (θ). (You can also drag the cannon barrel.) Make adjustments until the monkey catches the banana. What were the velocity and angle that you used? Without moving the cannon, I set the velocity to 17m/s and changed the angle to 32°. The monkey caught the banana right before they hit the ground. 3. Now try increasing and decreasing the velocity. Assuming the banana is moving fast enough to reach the tree, does the monkey still catch the banana? Describe your findings. This study source was downloaded by from CourseH on :44:55 GMT -05:00 This study resource was shared via CourseH GIZMOS Student Exploration Feed the Monkey (Projectile Motion) 2019 No matter what the velocity is, providing it’s at least enough to get the banana to the monkey when it reaches the ground, the banana will reach the monkey because the cannon is aimed at it. Presuming the monkey drops at the moment the banana is ejected, only aiming the cannon straight at the monkey will result in a collision. If the cannon aimed is under the monkey, the banana will fly under it and miss it. The same will happen for if the cannon is aimed above the monkey; it will fly over it. This study source was downloaded by from CourseH on :44:55 GMT -05:00 This study resource was shared via CourseH 2019 Activity A: Banana catchers Get the Gizmo ready:  Click Reset ( ).  Set the initial velocity (vInitial) to 26.0 m/s. Question: Where should you aim to hit the monkey with a banana? 1. Experiment: Turn on Show target line. Experiment with the Gizmo, trying several different cannon locations and launch angles. Try aiming above, below, and directly at the monkey. A. What always happens when you aim above the monkey’s head? If you aim above the monkey’s head, the banana always flies over top of it. B. What always happens when you aim below the monkey’s feet? The banana will always reach the ground before the monkey, meaning the monkey can never catch it. C. What always happens when you aim at the monkey’s body? Providing the velocity is enough to get the banana to the monkey at least when it reaches the ground, the monkey will always catch it. 2. Predict: How do you think changing the banana velocity will affect your results? Changing the velocity of the cannon will only change when the banana reaches the monkey. A greater velocity means that the banana will get to its target sooner. If the velocity is too slow, however, the banana will not have enough force acting on it to get to the monkey. 3. Test: Click Reset. Turn on Show grid, and drag the cannon to the point (25, 0.0) on the grid. Aim the cannon at the monkey, and try vInitial values of 15.0, 20.0, 25.0, and 30.0 m/s. How did the banana velocity affect the results of the experiment? As predicted, the velocity of the banana only changes how soon the banana will reach the monkey. The bigger the velocity the sooner the banana reaches its target. 4. Observe: Click Reset, and turn on Show path. Drag the cannon to (0.0, 16.0) so that it is at the same level as the monkey. Set vInitial to 25.0 m/s, and θ to 0.0 degrees. Click Play. The lines represent the trajectories, or paths, of the banana and monkey. The dots on the lines show positions every 0.15 seconds. Compare the dots for the banana and monkey. A. What do you notice about the height of the dots on each trajectory? The height of the dots on each trajectory are the same. This makes sense because both the monkey and the banana are experiencing the same downward acceleration. B. At any given time, what can you say about the heights of the banana and monkey? This study source was downloaded by from CourseH on :44:55 GMT -05:00 This study resource was shared via CourseH 2019 At any given time, you can say that the heights of the banana and the monkey are the same if they are falling from the same initial height. This study source was downloaded by from CourseH on :44:55 GMT -05:00 This study resource was shared via CourseH 2019 Activity B: Velocity vectors Get the Gizmo ready:  Click Reset, and drag the cannon to the ground.  Turn off Show grid and Show path.  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? 1. Observe: Turn on Show velocity components, and set θ to 45.0 degrees. Click Play, and focus on the blue and red arrows that represent the vertical and horizontal components of the banana’s velocity. A. As the banana flies through space, what do you notice about the blue (vertical) arrow? When the cannon is aimed upward, the blue arrow becomes shorter and shorter until it flips horizontally, showing when the banana is rising versus when it’s falling. When the cannon is aimed straight at the monkey, the arrow, facing down, starts very short but becomes gradually longer as the banana falls. B. As the banana flies through space, what do you notice about the red (horizontal) arrow? The red arrow stays the same length because an object will move at the same speed until an external force acts on it, such as when gravity pulls down the banana and it hits the ground or when the monkey grabs it, preventing it from continuing its path. C. Try other velocities and launch angles. Do these results hold up? These results hold true for every angle and distance. 2. Calculate: You can use trigonometry to find the initial horizontal and vertical components of the banana’s velocity. Take out your calculator now. Click Reset, and turn off Show velocity components. Set vInitial to 20.0 m/s and θ to 60.0 degrees. A. To calculate vx, multiply vInitial by the cosine of the angle: vx = vInitial • cos(θ): 10 m/s B. To calculate vy, multiply vInitial by the sine of the angle: vy = vInitial • sin(θ): 17.32 m/s C. Turn on Show velocity vectors. Were you correct? Yes, the results wer