(c) Suppose that
L
is a line tangent to the boundary of the golf green and parallel to the path of the ball. Let
Q
be the
point where the line is tangent to the circle. Notice that there are two possible positions for
Q
. Find the possible
x

coordinates of Q:
smallest
x
coordinate =
21.20
21.2
largest
x
coordinate =
21.20
21.2
10/31/2016
hw02S2.1
10/11
7.
2/4 points 
Previous Answers
A Ferris wheel of radius 100 feet is rotating at a constant angular speed
ω
rad/sec counterclockwise. Using a stopwatch, the
rider finds it takes
4
seconds to go from the lowest point on the ride to a point
Q
, which is level with the top of a 44 ft pole.
Assume the lowest point of the ride is 3 feet above ground level.
Let
Q(t)=(x(t),y(t))
be the coordinates of the rider at time
t
seconds; i.e., the parametric equations. Assuming the rider begins
at the lowest point on the wheel, then the parametric equations will have the form:
x(t)=r
cos(
ω
t
π
/2
) and
y(t)=r
sin(
ω
t 
π
/2
),
where
r
,
ω
can be determined from the information given. Provide answers below accurate to 3 decimal places. (Note: We have
imposed a coordinate system so that the center of the ferris wheel is the origin. There are other ways to impose coordinates,
leading to different parametric equations.)
(a)
r
=
100
100
feet
(b)
ω
=
0.628
0.235
rad/sec
(c) During the first revolution of the wheel, find the times when the rider's height above the ground is 80 feet.
first time =
5.6
5.7
sec
second time=
12.4
21
sec
10/31/2016
hw02S2.1
11/11
8.
3/3 points 
Previous Answers
SCalcET7 10.1.033.
Find parametric equations for the path of a particle that moves along the circle
in the manner described.
(Enter your answer as a commaseparated list of equations. Let
x
and
y
be in terms of
t
.)
(a) Once around clockwise, starting at (
4
,
2
).
$$
x
=4
cos
(
t
),
y
=2−4
sin
(
t
)
(b)
Two
times around counterclockwise, starting at (
4
,
2
).
$$
x
=4
cos
(
t
),
y
=4
sin
(
t
)+2
(c) Halfway around counterclockwise, starting at (0,
6
).
$$
x
=−4
sin
(
t
),
y
=4
cos
(
t
)+2
Solution or Explanation
Click to View Solution
x
2
+ (
y
−
2
)
2
=
16
0 ≤
t
≤ 2
π
.
0 ≤
t
≤
4
π
.
0 ≤
t
≤
π
.