Projectile Motion Lab Handout-Get Answer Now

Click on the “Projectile Motion Simulation” link to perform simulations in the setup satisfying the given conditions.

Click on the Lab tab. Change the Gravity to 9.80 m/s2.. Keep the height of the cannon at ground level.

Determine what angles you must have the cannon tilted at to have the cannon ball land at the target 20.5 m away when you have an initial speed of 20 m/s using the simulation. Let the mass of the cannon ball remain at 17.60 kg and the diameter at 0.18 m. Then use the Range formula to verify the angles. (Hint: recall from Trigonometry that sine can be positive in Quadratic I and Quadrant II—Use the Reference Angle Theorem). Ask you instructor if you have any trouble verifying the angle with the Range formula.

Use the Time, Range, and Height tool to determine the total amount of time the cannon was in the air (slide the tool to the landing point to list the time the cannon took to reach the ground). Use the equations from Chapter 3 to verify the time it takes the cannon to reach the ground.

Now change to initial velocity to 15 m/s. Find the angle that will allow for the maximum horizontal displacement when the object is launched at the same level it will land.

Now try changing the object to a different object (with a different mass and shape). Compare the trajectory of both motions. You can try several different objects with various mass and size. Are the trajectories different (different horizontal distance, different maximum heights, etc.) for each of the objects? Does mass play a role in the launch given that the objects leave with the same initial velocity?

Next raise the stand of the cannon (click on the base of the cannon at move it) to 5.0 m.

With an initial velocity of 25.0 m/s and at an angle of 25 degrees, determine how far (horizontally) the cannon ball will land. Use the equations from Chapter 3 to verify the horizontal displacement.

Determine the horizontal and vertical components of the initial velocity. Use the horizontal and vertical components of the initial velocity to verify that the initial velocity is 25.0 m/s and that the angle is 25 degrees.

Determine the maximum height by sliding the time, range, and height measure to the point at the maximum height. Use the equations from Chapter 3 to verify this maximum height.

How long does it take to reach the maximum height? Use the equations from Chapter 3 to verify the time that the time, range, height tool reads.

Next we will study the effects of air resistance. Perform the following simulations to answer the following questions.

Click on the eraser to clear the trajectories. With the cannon selected at the automatic diameter setting, launch the cannon at an angle of 80 degrees. Next, click on the air resistance option to add air resistance. Without change any other setting for the cannon, launch the cannon. Is there much of a difference in the trajectories?

Now clear the trajectories using the eraser button. Increase the diameter of the cannon significantly. Launch the larger cannon at the same angle without air resistance to observe the trajectory. Next, launch the larger cannon at the same angle with air resistance. Is there much of a difference in the trajectories. Does increased surface area affect the amount of air resistance on an object?

Conceptual Questions:

For an object being launched at ground level at a tilted non-zero initial velocity, is the velocity zero anywhere? Are the horizontal or vertical components of the velocity zero at any point?

What is the shape of this trajectory? (Use the mathematical term).

If an object is launched with a strictly horizontal initial velocity, what is the vertical component of the initial velocity?

Will an object take longer, less, or the same amount of time to reach the ground if it is dropped from rest rather than launched with a strictly horizontal initial velocity? Try using the simulation to help you determine this. For the free fall simulation, have the cannon point downwards and set the initial velocity to 0 m/s. Use the time, range, height sliding tool to determine the amount of time it took for the cannon to reach the ground. For the horizontal launch, change the angle to 0 degrees and give the cannon an arbitrary non-zero initial velocity. Again use the time, range, and height sliding tool to determine the amount of time it takes for the cannon to reach the ground. Compare these times.

With a strictly horizontal launch (with an angle of 0 degrees from the horizontal), how does the initial velocity affect the trajectory (specifically the range)? Use the simulation to help you obtain your answer.

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