#56
How do you figure out how far the ball will reach and if jill will be able to catch it at the same time? Also, what is a trochoid and a hypocycloid?
posted by Elena at 7:04 PM
Sunday, April 29, 2007
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3 Comments:
I graphed xt1=100+20cos(.7t) yt1=20+20sin(.7t) xt2=62cos(1.2)t and yt2=5+62sin(1.2)t-16t^2. Then I looked at the table to see if the distance for jill(xt1) and the distance for the ball(xt2) were within 2 ft of each other at any point in time. I changed the velocity and the angle for the ball little by little until xt1 and xt2 were within 2 feet at any one point, and I finally found success: when the ball's velocity is 60 and the ball's angle is 1.5 radians, the two are about 1.2 feet apart (at time=3.5 seconds). I hope I did this right. It was all guess and check for me, so maybe someone else has a better method.
a trochoid is "a curve traced by a point on or connected with a circle as the circle rolls along a fixed straight line." and a hypocycloid is "a line generated by a point on a circle that rolls around inside another circle."
The point of the problems with weird curves is that they define the terms trochoid and hypocycloid . So not knowing those terms in advance is not an impediment to doing the problem.
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