point with chalk. She then rides the bike along a flat, level road. She imposes a coordinate system as
shown in the figure below such that the chalk mark is touching the ground at the point (0,0) at time
t=0
. The radius of her wheels is 35 cm and the bike moves at 70
π
cm/sec in the direction indicated. As
the bike moves from left to right in the picture below, the chalk mark will trace out a path in the
imposed coordinate system:
The parametric equations for the path of the chalk mark are
x
(
t
) = 70
π
t
+ 35cos(–2
π
t
–
π
/2)
y
(
t
) = 35 + 35sin(–2
π
t
–
π
/2)
A portion of the path (on the time interval [0,2]) is shown in this figure:
Give EXACT ANSWERS to all questions below; use pi to denote the number
π
(a) The horizontal velocity is
.
.

2/21/14, 2:44 PM
Chapter 3.5 HW
Page 11 of 14
(b) The vertical velocity is
(c) Compute
x'(t)
at these times:
t = 0
sec
t = 0.25
sec
t = 0.5
sec
t = 0.75
sec
t = 1
sec
(d) Compute
y'(t)
at these times:
t = 0
sec
t = 0.25
sec
t = 0.5
sec
t = 0.75
sec
t = 1
sec
(e) When is the first time the horizontal velocity will be a maximum?
(f) When is the first time the horizontal velocity will be a minimum?
(g) What is the maximum horizontal velocity?
(h) What is the minimum horizontal velocity?
.

2/21/14, 2:44 PM
Chapter 3.5 HW
Page 12 of 14
(i) When is the first time the vertical velocity will be a maximum?
(j) When is the first time the vertical velocity be a minimum?
(k) What is the maximum vertical velocity?
(l) What is the minimum vertical velocity?
(m) The speed of the moving chalk mark at time
t
is defined by the equation
s
(
t
) =
{(
x
'(
t
))
2
+ (
y
'(
t
))
2
}.
Compute s(t).
(n) During the first 2 seconds, how many times will the speed be equal to 50 cm/sec?
11.
14/14 points |
Previous Answers
An object is moving in the plane according to these parametric equations:
x
(
t
) =
π
t
+ cos(4
π
t
+
π
/2)
y
(
t
) = sin(4
π
t
+
π
/2)
A portion of the "cycloidal" path (on the time interval [0,1]) is shown in this figure:
At time
t=0
, the object is located at (0,1). Give EXACT ANSWERS to all questions below; use pi to
denote the number
π
(a) The horizontal velocity is
(b) The vertical velocity is
.
.
.
√

2/21/14, 2:44 PM
Chapter 3.5 HW
Page 13 of 14