(g) The slope of the tangent line at time t=1/3 seconds is
$$
−
35
√
3
.
(h) Recall, the speed of the object at time t is given by the equation:
s(t)=
√
[x '(t)]
2
+ [y ' (t)]
2
m/s.
The speed of the object at time t=1/3 seconds is
$$
π·√
52
·
(34)+32
·
(14)
.
(i) The first time when the horizontal and vertical velocities are equal is time t=
$$(1
π
)
·
atan(
−
35)+1
.
(j) Let Q be the position of the object at the time you found in part (i). The slope of the tangent line to the ellipse
at Q is
$$1

12/14/16, 4(10 PM
hw13S10.2
.
11.
3/3 points |
Previous Answers
A 4-centimeter rod is attached at one end A to a point on a wheel of radius 2 cm. The other end B is free to move back
and forth along a horizontal bar that goes through the center of the wheel. At time t=0 the rod is situated as in the
diagram at the left below. The wheel rotates counterclockwise at 3.5 rev/sec. Thus, when t=1/21 sec, the rod is situated
as in the diagram at the right below.
(a) How far is the right end of the rod (the point B) from the center of the wheel at time t=1/21 sec?
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Page 10 of 12
12.
18/18 points |
Previous Answers
This question builds on an earlier "rod problem": A 4-centimeter rod is attached at one end A to a point on a wheel of
radius 2 cm. The other end B is free to move back and forth along a horizontal bar that goes through the center of the
wheel. At time t=0 the rod is situated as in the diagram at the left below. The wheel rotates counterclockwise at 3.5
rev/sec. Thus, when t=1/21 sec, the rod is situated as in the diagram at the right below.

(b) Express the x-coordinate of the right end of the rod as a function of t:

(c) Express the speed of the right end of the rod as a function of t:

12/14/16, 4(10 PM
hw13S10.2
(a) Let P be the point on the circle where the rod is attached. Write a formula for the slope of the tangent line to
the circle at time t seconds:

Page 11 of 12
(b) Write a formula for the slope of the rod at time t seconds: (Hint: You will need to recall the formula for the x-