Physics 101

This lab investigates the nature of motion in 2 dimensions through the use of ballistic trajectories produced by a virtual cannon. An important part of this lab is to measure X,Y coordinates (done by left click on the background grid). Also important is the Time Aloft readout which measures total time in the air of the cannonball. This lab has many parts to it (similar to the momentum lab) and will require loading new cannons that will give you different default controls. The link to each cannon is given below in the various experimental procedure parts. Close the previous cannon before getting a new one. Mouseover the topics below for further instructions. Note that you might experience some screen flicker during the cannon shots.

Part I: Hitting the monkey.

1. Without changing any of the controls, hit the fire button and observe what happens. Provide a qualitative explanation of why the cannon ball and the monkey both hit the ground at the same time.

2. Hit the reset button and change the angle from 30 to 60 degrees using the slider bar. In this case, predict whether the monkey or the cannon ball will hit the ground first. Fire to verify your prediction and then explain the result.

3. The platform of the monkey is 400 meters off the ground and its located at an X position of 725 meters from the cannon. What is the X,Y position of the middle of the monkey? (note - this is a damn big monkey!) Suppose you want to hit the middle of monkey after its falling for 4 seconds. What must be the X,Y cooordinates of the cannon ball after 4 seconds?

4. Reset and change the velocity to 200 m/s. Click the snapshots button. In shaphot mode, the time between each black dot is 1 second. Determine what angle will actually hit the monkey as its falling. Just use your eye to observe if the cannon ball intersects the monkey figure as its falling. Explain why that angle works at that velocity but other angles down work. What was the approximate travel time of the shot that hit the monkey while it was falling?

5. Now explain the conditions in terms of the properties of the trajectory of the projectile that would be needed to hit the monkey precisely when it hits the ground? Try and do this and report in your firing solution on the worksheet.

Hitting a Fixed Target
The total horizontal range of a projectile is given by

R = 2*(V Cosine Angle)(V Sine Angle)/g
where g = 9.8 meters per second²

A) The distance from the cannon to the monkey is 725 meters. Do the math and determine the velocity that will hit the target for angles of 20, 40,60 and 80 degrees and then verify your results.

If your shooting at the enemy, which of these firing solutions would you use and why? (Note you want the cannonball to land at 725 which you can verify with cursor measurement of position - the monkey itself is really really big and will blow up if the cannonball gets sufficiently close.)

B) Set the angle to 60 degrees and the velocity to 75 and fire. What is the horizontal distance traveled? What is the maximum vertical height? Set the angle to 30 degrees and repeat those two measurements. Can you find a relation between total horizontal range and maximum height?

C) Its always useful to blow one's self up. Set the angle to 89 degrees and the velocity to 32. From the lecture notes, figure out what the maximum height would be? Use this value to verify that the time aloft is approximately correct.

Part III: Hitting a target in the wind.

1. In real life, on the earth, we shoot at our enemy through at atmosphere, so there will be frictional drag. Hit reset to clear any old trajectories. Set the angle to 45 and the velocity to 70. click the buttons that say snapshots and Vectors. Fire and note the distance and also measure the coordinate length of the X-vector (the purple one).

Now click the button that says drag. This means we are shooting into an atmosphere. Click fire again and explain why the projectile now falls short compared to the previous case). Describe what is happening to the length of the X-vector as a function of time now (each black dot in the snap shot represents 1 second of flight).

3. Now set the wind to -30 mph and change the radius of the projectile to 2 cm. Adjust the angle and velocity until you hit the target. Keeping the velocity fixed determine what range of angles hit the target. Now qualitatively explain why there are more firing solutions available to hit targe than if you were to shoot the cannon in a vacuum at this fixed velocity.

4. Now set the angle to 62 degrees and the velocity to 200 and the radius to 4 cm. Set the wind to 0 and the gravity down to 2. Fire the cannon (you will not hit the monkey). Explain why the projectile, after it reaches the apex of its trajectory is not really accelerating back down towards the planetary surface. The cut away graph in the upper left shows the X and Y components of the velocity as a function of time (the orange dots are for the monkey which has velocity of zero). Examine this to help with your explanation.