Question

**QUESTION 1**. A ferris wheel has a radius of 12
m. The center of the ferris wheel is 14 m above the ground. When it
is rotating at full speed the ferris wheel takes 10 s to make a
full turn. We can track one seat on the ferris wheel. Let’s define
t = 0 to be a time when that seat is at the top of the ferris wheel
while the ferris wheel is rotating at full speed. (a) Write a
function which describes the height of the seat above the ground as
a function of time. You should show your reasoning behind
constructing this function. At a bare minimum you should probably
explain • What are the maximum and minimum heights of the seat? •
What is the period of the function? • What is the initial value of
the function? (b) The seats on this ferris wheel are separated by
an angle of 15 ◦ around the ferris wheel. Write the functions
describing the heights as functions of time for the seats
immediately “ahead” and immediately “behind” the seat that you
wrote the function for in 2a. (c) The ferris wheel has a frame that
is a big circle of radius 12 m. The hinges that support the seats
are attached directly to this frame. What is the distance, as
measured alone the frame, between hinge supporting one seat and the
next one along the ferris wheel? A sketch will probably help you to
solve this and will also help you to explain your solution. (d)
What is the straight line distance between a hinge supporting a
seat and the next one along the ferris wheel? Again, a sketch will
be very helpful.

**QUESTION 2**. In a physics lab, a mass on the end
of a spring is being monitored with a motion sensor (basically a
small sonar). It oscillates with a height above the motion sensor
as a function of time which is described by y ( t ) = (0 . 07) sin
[ 2 π/ 0 . 8 ( t − 0 . 4) ] + 0 . 13 where y is in meters and t is
in seconds. (As a physicist it makes me cringe to not include units
in the equation. But mathematicians don’t like units messing up
nice clean mathematical expressions, so I’ll do it their way in
this course.) (a) What is the period of this oscillation? (b) Do a
detailed sketch of a y vs. t plot of this oscillation. By a
detailed sketch I mean that it should have numbers on both axes so
that anyone looking at the plot should be able to determine the
period, maximum and minimum values of y , and times when y is at a
maximum or minimum value. Show at least two full oscillations in
the sketch. (c) BONUS: write the function which describes the
velocity (technically the y-component of velocity) of the mass as
function of time. Show how you got it.

**QUESTION 3**

A person is standing 12 meters away from a streetlight. They observe that they cast a shadow that is 3.5 meters

long. If a ray of light from the streetlight to the tip of the persons shadow forms an angle of 27.5with the ground,how tall is the person and how tall is the streetlight

A person is standing 12 meters away from a streetlight. They observe that they cast a shadow that is 3.5 meters

long. If a ray of light from the streetlight to the tip of the persons shadow forms an angle of 27.5◦ with the ground,how tall is the person and how tall is the streetlight

QUESTIONS SOLVED SHOULD BE PROPERLY LABELED CORRESPONDING TO EACH ANSWER

Answer #1

A ferris wheel is 10 meters in diameter and boarded from a
platform that is 4 meters above the ground. The six o'clock
position on the ferris wheel is level with the loading platform.
The wheel completes 1 full revolution in 6 minutes. The function
h = f(t) gives your height in meters above the ground
t minutes after the wheel begins to turn.
What is the Amplitude? _________ meters
What is the Midline? y = _________ meters
What is...

A ferris wheel is 25 meters in diameter and boarded from a
platform that is 1 meters above the ground. The six o'clock
position on the ferris wheel is level with the loading platform.
The wheel completes 1 full revolution in 4 minutes. The function h
= f(t) gives your height in meters above the ground t minutes after
the wheel begins to turn. Write an equation for h = f(t).

A Ferris wheel is 20 m in diameter and makes 1 revolution every
3 minutes. This Ferris wheel has a 3 meters boarding platform with
riders entering at the bottom. At time t = 0 Chris is at the top of
the ride, descending.
Find all the times at which Chris is 15 meters above the
ground.

A ferris wheel, whose center is 16 yards above the
ground, has a radius of 25 yards. The ferris wheel starts at the
three o'clock position and moves counterclockwise. The ferris wheel
moves at 3 radians per second. A) Define a model (using function
notation) for the horizontal position of the ferris wheel (in
yards) relative to the vertical midline of the wheel, in terms of
time elapsed (in seconds) B) Graph the function from part
A)

1.Find a possible formula for the trigonometric function whose
values are in the following table.
x
0
2
4
6
8
10
12
y
-2
-5
-2
1
-2
-5
-2
y=
2. A population of rabbits oscillates 21 above and below an
average of 103 during the year, hitting the lowest value in January
(t = 0). Find an equation for the population, P, in terms
of the months since January, t.
P(t) =
What if the lowest value...

1) 2 point charges are separated by a distance of 8 cm. The left
charge is 48 mC and the right charge is -16mC. Using a full sheet
of paper: draw the 2 charges separated by 8cm, centered in the
sheet. (if you are missing a ruler estimate 8cm as ⅓ a paper sheet
length). [6] a) Draw field lines to indicate the electric fields
for this distribution. [4] b) Draw 3 equipotential surfaces, 1
each, that pass: -Through the...

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