ground after 2.0 seconds. a. What is the initial x-component of velocity when the projectile is initially fired? What is the initial y-component of th...
Projectile motion Investigation 6B: Projectile motion Projectile motion occurs whenever a moving object is under no force except gravity. The equations of motion for each coordinate axis are different—and independent of each other—so you can analyze them separately. What projection angle will shoot a cannonball the farthest?
Part 1: What angle launches projectiles the maximum distance? 1. Using your computer, click on the interactive simulation in the electronic resources to conduct the investigation. Set the magnitude of the velocity vr0 to 25 m/s. 2. Try different projection angles, such as θ0 = 10°, 20°, 30°, and so on. 3. For each, press [Run] to see the trajectory and inspect x to see how far it goes. Questions a. What projection angle θ0 shoots the cannonball the furthest? ____
Tabulate your data.
Table 1: Launch angle (initial velocity 25 m/s) θ0 Range Provide a conceptual explanation for why you think this angle gives the maximum range.
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b. Find two additional different initial velocities and angles that give the exact same time in the air as in (a). What is the same about these three cases (in addition to time t)?
Table 2: Time in air
Case
vr0 (m/s)
1
25
θ0
vx0 (m/s)
vy0 (m/s)
t (s)
2 3 Part 2: Hitting a target with projectile motion 1. 2. 3. 4.
Select “Easy” using the button. Press [Reset] to generate a new target. Set the components of the initial velocity using either Cartesian or polar coordinates. Press [Run] to see the trajectory. Modify the velocity as necessary to hit the target.
Questions a. Explain the difference between Cartesian and polar coordinates.
b. Sketch the shapes of the graphs of x and vx versus time. Why do the graphs have these shapes?
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Sketch the shapes of the graphs of y and vy versus time. Why do the graphs have these shapes?
c. Select “Hard” and press [Reset] to generate an elevated target. Can you hit it?
Part 3: Projectile motion off the edge of a table 1. Set carbon papers on a length of white craft paper on the floor next to a table. 2. Roll a marble five times down a ramp (such as an inclined textbook) from the same starting point. Measure the vertical height and average horizontal distance traveled by the marbles through the air. Questions a. Why is carbon paper useful for this investigation? b. Use the projectile motion equations to calculate the marble's velocity when leaving the table. Show your work below.
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Applying new knowledge 1. What is special about the x-component velocity for a projectile?
2. What does vy represent? Is it constant for projectile motion? 3. What causes the difference between the x and y position graphs for a projectile?
4. A projectile is fired horizontally off the top of a cliff with an initial velocity of 30 m/s. It hits the ground after 2.0 seconds. a. What is the initial x-component of velocity when the projectile is initially fired? What is the initial y-component of the velocity?
b. How far from the base of the cliff does the projectile land? (Hint: How far does it go in the x direction?)
c. How high is the cliff? ( Hint: How far does the projectile go in the y-direction?)
5. A projectile is shot at an angle of 45° with velocity components vx and vy both equal to 10 m/s. Sketch the trajectory of the projectile.
6.
Write a multiple-choice problem on a projectile launched horizontally. Given the initial velocity and the time in the air, the reader must correctly identify the final velocity components, vx and vy.
