The accompanying figure shows a right circular cylinder of radius 10 cm spinning at 3 revolutions per minute about the z -axis. At time t = 0 s, a bug at the pint 0 , 10 , 0 begins walking straight up the face of the cylinder at the rate of 0.5 cm/min. (a) Find the cylindrical coordinates of the bug after 2 min. (b) Find the rectangular coordinates of the bug after 2 min. (c) Find the spherical coordinates of the bug after 2 min.
The accompanying figure shows a right circular cylinder of radius 10 cm spinning at 3 revolutions per minute about the z -axis. At time t = 0 s, a bug at the pint 0 , 10 , 0 begins walking straight up the face of the cylinder at the rate of 0.5 cm/min. (a) Find the cylindrical coordinates of the bug after 2 min. (b) Find the rectangular coordinates of the bug after 2 min. (c) Find the spherical coordinates of the bug after 2 min.
The accompanying figure shows a right circular cylinder of radius 10 cm spinning at 3 revolutions per minute about the z-axis. At time
t
=
0
s, a bug at the pint
0
,
10
,
0
begins walking straight up the face of the cylinder at the rate of 0.5 cm/min.
(a) Find the cylindrical coordinates of the bug after 2 min.
(b) Find the rectangular coordinates of the bug after 2 min.
(c) Find the spherical coordinates of the bug after 2 min.
A very tall light standard is swaying in an east-west direction in a strong wind. An observer notes that the time difference between the vertical position and the furthest point of sway was 2 seconds. The pole is 40 metres tall. At the furthest point of sway, the tip of the pole is 1° out of the vertical position when measured from the bottom of the pole. Create a sinusoidal equation that models the motion of the tip of the pole as a displacement from the vertical position as a sinusoidal function of time. Assume time starts when the tip of the pole is furthest east. Include a sketch of the graph of your equation. (4 marks)
At the instant shown, the arm OA of the conveyor belt is rotating
about the z axis with a constant angular velocity w₁ = 6.1 rad/s,
while at the same instant the arm is rotating upward at a constant rate
W₂ = 4.2 rad/s. (Figure 1)
Figure
091
r = 6 ft
0-45°
< 1 of 1
If the conveyor is running at a constant rate=5 ft/s, determine the velocity of the package P at the instant shown. Neglect the size of the package.
Enter the x, y, and z components of the velocity in feet per second to three significant figures separated by commas.
Vp =
Submit
Part B
195] ΑΣΦ". 41
ap=
Request Answer
vec +
ĊIP ?
Determine the acceleration of the package P at the instant shown.
Enter the x, y, and z components of the acceleration in feet per second squared to three significant figures separated by commas.
AΣo↓ vec ↑
B
ft/s
?
ft/s²
- A robot arm joint moves in an elliptical path (horizontal major axis 8.0 cm, minor axis
4.0 cm, center at origin). The joint moves such that
dy
2.5 cm/s. Find its
%3D
dx
instantaneous velocity when the joint is positioned at coordinates (0,4). This elliptical
path is given by
64
y?
1.
16
University Calculus: Early Transcendentals (3rd Edition)
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