Calculus BC
Parametric Goodness.
Name___________________________
1. Ron is on a ferris wheel of radius 35 ft. that turns counterclockwise at the rate of
one revolution every 12 sec. The lowest point of the ferris wheel is 15 ft. above
the ground level. Find parametric equations for the position of Ron as a function
of time if the ferris wheel starts ( at time t=0) with Ron at point (35, 50).

x(t )  35cos t
6

y (t )  50  35sin t
6
2. Nancy hits golf balls off the practice tee with an initial velocity of 180 ft/sec with
4 different clubs. How far down the fairway does the ball hit the ground if it
comes off the club making an angle with the with horizontal of
a. 15º
b) 30º
506.25 ft
876.851 ft
In exercises 7- 12, write a parameterization for the curves in the xy-plane.
Remember, to go the opposite direction in your circle, you can put a negative with either
coordinate if it does not tell you where to start. Or you can switch the sin and the cos. If
it tells you a starting point(like number 6), then you have to put the negative with the cos
because that is the x.
3. A circle of radius 3 centered at the origin and traced clockwise.
x(t )  3cos t y (t )  3sin t
4. A vertical line through the point (-2,-3)
x(t )  2 y (t )  3t
5. A circle of radius 5 centered at the point (2,1) and traced counterclockwise.
x(t )  2  5cos t y (t )  1  5sin t
6. A circle of radius 2 centered at the origin traced clockwise from (-2,0) when t=0
x(t )  2 cos t y (t )  2sin t
7. A line through the points (2, -1) and (1,3),
x(t )  2  t y (t )  1  4t
8. An ellipse centered at the origin and crossing the x axis at  5 and the y axis at
 7.
x(t )  5cos t y(t )  7 sin t
a) 229 total miles traveld from t=0 to t=40
b) Since v(t) is differentiable, that implies that v(t) is continuous. There will be 2
times. Per MVT, since f(0)=f(15)=7, then there exists a c on the interval (0,15)
such that f (c)  0 . Since the derivative of the char is the acceleration, this is
instance one. Also by MVT, since f(25)=f(30)=2.4, then there exists a c on the
interval (25, 30) such that f (c)  0 .
c) f (23)  .408 miles / min 2
d) Average Velocity = integral from 0 to 40 divided by 40 .
40
1
f (t )dt  5.916 miles / min
40 0