A Ferris wheel is 200 ft in diameter with its lowest point 3 ft off the ground. Once all the passengers have been loaded, the wheel makes one full rotation counterclockwise in 3 min . Suppose that a couple is seated at the lowest point on the wheel and are the last passengersr to be loaded. a. Write a model representing the couple's horizontal position x (in feet) relative to the center of the Ferris wheel, t minutes after the ride starts. b. Write a model representing the couple's height y (in feet) above ground level, t minutes after the ride starts. c. Give the coordinates of the couple's position 2 min into the ride and describe the position.
A Ferris wheel is 200 ft in diameter with its lowest point 3 ft off the ground. Once all the passengers have been loaded, the wheel makes one full rotation counterclockwise in 3 min . Suppose that a couple is seated at the lowest point on the wheel and are the last passengersr to be loaded. a. Write a model representing the couple's horizontal position x (in feet) relative to the center of the Ferris wheel, t minutes after the ride starts. b. Write a model representing the couple's height y (in feet) above ground level, t minutes after the ride starts. c. Give the coordinates of the couple's position 2 min into the ride and describe the position.
Solution Summary: The author calculates the couple's horizontal position x relative to the centre of the Ferris wheel.
A Ferris wheel is
200
ft
in diameter with its lowest point
3
ft
off the ground. Once all the passengers have been loaded, the wheel makes one full rotation counterclockwise in
3
min
. Suppose that a couple is seated at the lowest point on the wheel and are the last passengersr to be loaded.
a. Write a model representing the couple's horizontal position
x
(in feet) relative to the center of the Ferris wheel,
t
minutes after the ride starts.
b. Write a model representing the couple's height
y
(in feet) above ground level,
t
minutes after the ride starts.
c. Give the coordinates of the couple's position
2
min
into the ride and describe the position.
1. Show that the vector field
F(x, y, z)
=
(2x sin ye³)ix² cos yj + (3xe³ +5)k
satisfies the necessary conditions for a conservative vector field, and find a potential function for
F.
1. Newton's Law of Gravitation (an example of an inverse square law) states that the magnitude
of the gravitational force between two objects with masses m and M is
|F|
mMG
|r|2
where r is the distance between the objects, and G is the gravitational constant. Assume that the
object with mass M is located at the origin in R³. Then, the gravitational force field acting on
the object at the point r = (x, y, z) is given by
F(x, y, z) =
mMG
r3
r.
mMG
mMG
Show that the scalar vector field f(x, y, z) =
=
is a potential function for
r
√√x² + y² .
Fi.e. show that F = Vf.
Remark: f is the negative of the physical potential energy, because F = -V(-ƒ).
2. Suppose f(x) = 3x² - 5x. Show all your work for the problems below.
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