Physics Simulation

The Boat and Plane Problem

BHS -> Staff -> Mr. Stanbrough -> AP Physics -> Kinematics -> this page

An airplane is flying horizontally at a constant speed of __v__ m/s at an altitude of __h__ meters. The pilot must drop a package to a 20 m long yacht in the water below. At what horizontal distance from the yacht should the pilot release the package so that the package lands on the yacht? Ignore air resistance effects.

Here is a method for setting up an Interactive Physics simulation to solve this problem:

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The Simulation:

1. Open the Interactive Physics program.
2. Set the simulation accuracy to "Accurate".
3. Create a rectangle object () to represent the boat.
4. The boat needs to be 20 m long, so:
   1. Select "Rulers" from the Workspace submenu of the View Menu.
   2. Zoom out () a couple of times so that you see at least 20 meters in the window.
   3. Drag the rectangle so that it is about 20 m long. (It doesn't have to be exact.)
5. Anchor () the boat. (We don't need it to float away...)
6. Open the Properties Window for the boat, and set its position to (0, 0).
7. Create a circle object () to represent the package dropped by the plane.

8. Sample Properties Window for the "boat"
   Sample Properties Window for the "Package". Here, h = 100 m and v = 15 m/s. The current guess for the "drop distance" is x - 30 m.

   Open the Properties Window for the circle object and set:
   1. x = your starting guess for the release distance.
   2. y = the "h" value from the problem
   3. v_x = - the "v" distance from the problem. (Note the negative sign.)
9. Zoom out () until you can see both the "boat" and the "package".
10. Of course, you can turn on Trace (World Menu) if you want to record the path of the package.

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Running the Simulation:

Run the simulation, and adjust the x value for the package until you get the package to hit the boat.

It might happen that instead of hitting the boat, the package passes right through the boat! Interactive Physics will only detect collisions if the objects actually overlap in space at the end of a time step. If the package is going fast enough that the boat and the package never actually overlap, no collision will be detected. What to do? Go to the Accuracy dialog (in the World Menu) and reduce the time step by half - then try again. Keep reducing the time step until you get a collision.

Actually, this is a good practice for any numerical simulation - keep halving the time step until the results from one run to the next don't differ by an appreciable amount. Then, you can be reasonably confident that you have the most accurate result for a given setup.

When you have results that you are happy with, use the text tool () to add your name, and print it out. Turn it in, along with your analytical solution, of course.

This is a screen shot of a "semi-fancy" version of this simulation, in which an "airplane" actually flies over and drops the "package" to the "boat". Physically, it doesn't provide any additional information than the plain version.