Derivative - Radar

This applet challenges the user to sketch the derivative of a function whose graph (in blue) is given. Starting to the left of the y-axes, drag the mouse slowly all the way to the right (past x = 19) to make your sketch in red. Since it is hard to estimate magnitude of slopes, you are given the following hint - between any two consective points where the slope is zero, the steepest slope will be plus or minus 2.

This procedure can be applied to radar as follows. Suppose a target is moving back and forth, toward and away from your radar unit. The given function represents the distance as a function of time as measured by your radar. (Positive position indicates the target is in front of you, negative behind.) Then the derivative function will tell you velocity at any time.

Try drawing the graph of the derivative. Then click the "Answer (derivative)" button to see how close you were (the correct curve will be drawn in green). Or, if you like, you can look at the answer without trying it yourself. If you've tried it yourself and looked at the answer, the "Error" button will show you the (unsigned) area between the curves. An error of less than 4 is quite good. Try it with other initial curves using the "New start" button. When you think you have a good feel for sketching the derivative, try filling in the "lab report" for the derivative.

The code for the applet above is online.

Here is a picture of a radar screen in use.

(An Air Traffic Controller watches his radar aboard the aircraft carrier USS Independence (CV 62) and monitors aircraft movement in the skies over the Arabian Gulf and southern Iraq. Independence is deployed to the Gulf in support of Operation Southern Watch. U.S. Navy photo by Photographer's Mate Airman Chris D. Howell. [980214-N-7355H-003] Feb. 14, 1998.)

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USNA Mathematics Department
Comments to: Professor Carol G. Crawford, at cgc@nadn.navy.mil or Professor Mark D. Meyerson, at mdm@nadn.navy.mil