Extra Practice Trig Application – Setting up Equations
Ferris Wheel
A Ferris wheel has a diameter of 20 m. The centre of the circle is 11 m off the ground. The Ferris
wheel makes a complete rotation in 30 seconds.
a)
Draw the graph of the height of a rider vs. time. The graph should have 2 cycles and the
graph should start when the rider boards the Ferris wheel. Determine an equation that
models the situation.
Height of
Rider (m)
Time (s)
(
b)
)
Draw the graph of the height of a rider vs. time. The graph should have 2 cycles and the
graph should start when the rider is at the top of the Ferris Wheel. Determine an
equation that models the situation.
Height of
Rider (m)
Time (s)
(
)
c)
Draw the graph of the height of a rider vs. time. The graph should have 2 cycles and the
graph should start when the rider is halfway between the highest and lowest point in
the Ferris wheel. The rider is heading towards the top of the Ferris wheel. Determine
an equation that models the situation.
Height of
Rider (m)
Time (s)
(
d)
)
Draw the graph of the height of a rider vs. time. The graph should have 2 cycles and the
graph should start when the rider is halfway between the highest and lowest point in
the Ferris wheel. The rider is heading towards the bottom of the Ferris wheel.
Determine an equation that models the situation.
Height of
Rider (m)
Time (s)
(
)
Tides
Height (m)
In Saint John, New Brunswick, the tides vary greatly during the day. During May, the predicted
height of the tides are 0.5 m at 4 am, 8.5 m at 10 am, 0.5 m at 4 pm, and 8.5 m at 10 pm.
a) Draw the graph of the height of the water in m, t hours after midnight. Determine an equation
that models the situation.
( (
))
b) Draw the graph of the height of the water in m, t hours after noon. Determine an equation
that models the situation.
The same graph and equation work for this situation as well!
During May, on the Outer Wood Island, New Brunswick, the predicted height of the tides are 0.7 m at
5:30 am, 5.5 m at 11:30 am, 0.7 m at 5:30 pm, and 5.5 m at 11:30 pm.
a) Draw the graph of the height of the water in m, t hours after midnight. Determine an equation
that models the situation.
Height (m)
( (
))
b) Draw the graph of the height of the water in m, t hours after noon. Determine an equation
that models the situation.
The same graph and equation work for this situation as well!
Approximate data was taken from www.waterlevels.gc.ca
Pendulum
1. A pendulum makes 10 complete swings per minute from points A to B then back to A again. The
distance between the points A and B, which are at the maximum end of the swing is 50 cm.
a)
Draw the graph of the horizontal distance of the pendulum from point A vs. time. The
graph should have 2 cycles and the graph should start from point B. Determine an
equation that models the situation.
Horizontal Distance from A (cm)
(
b)
)
Time (s)
Draw the graph of the horizontal distance of the pendulum from point B vs. time. The
graph should have 2 cycles and the graph should start from point A. Determine an
equation that models the situation.
The same graph and equation as above works! The difference will be that the y-axis is
“The horizontal distance of the pendulum from point B”
Draw the graph of the horizontal distance of the pendulum from point B vs. time. The
graph should have 2 cycles and the graph should start from the centre of the
pendulum, and swings towards B. Determine an equation that models the situation.
Horizontal Distance from B (cm)
c)
(
)
Time (s)
Draw the graph of the horizontal distance of the pendulum from point A vs. time. The
graph should have 2 cycles and the graph should start from point A. Determine an
equation that models the situation.
Horizontal Distance from A (cm)
d)
Time (s)
(
Horizontal Displacement from the centre (cm)
e)
)
Draw the graph of the horizontal displacement of the pendulum from the point directly
in the middle of A and B vs. time. Consider A to be a negative distance away from the
centre. The graph should have 2 cycles and the graph should start from point B.
Determine an equation that models the situation.
Time (s)
(
Draw the graph of the horizontal displacement of the pendulum from the point directly
in the middle of A and B vs. time. Consider A to be a negative distance away from the
centre. The graph should have 2 cycles and the graph should start from point A.
Determine an equation that models the situation.
Horizontal Displacement from the centre (cm)
f)
)
Time (s)
(
g)
)
Challenge Problem:
Draw the graph of the positive horizontal distance of the pendulum from the point
directly in the middle of A and B vs. time. The graph should have 2 cycles and the graph
should start from point B. Determine an equation that models the situation.
Horizontal
Distance from
the centre (cm)
Time (s)
|
(
)|
Because the graph is the positive horizontal distance of the pendulum, when the
pendulum is at A, it is +25 cm away from the centre. When the pendulum is at B,
it is also +25 cm away from the centre. At 1.5 s, the pendulum is moving the
fastest. At 0s, 3s, and 6s, the pendulum is at the ends of its swing, and it’s speed
is 0 cm/s.