Functions in Motion

A challenging task in which you are to recognize functions

in real-life situations

Directions Within your team, determine a time-

keeper, a team leader, and a recorder (*Note, not all of you will have a role)

You will switch roles after each example

Do NOT discuss any of the problems with other groups

If you have a question, ask the teacher

You will have ten minutes per problem

Good Luck!

Consider this…..

An object in launched directly upward at 64 feet per second (ft/s) from a platform 80 feet high. What will be the object's maximum height? When will it attain this height?

Note: you will need to know the equation: s(t) = –gt2 + v0t + h0equ

Gravity is 64 ft/sec

Consider this….

A bicyclist is pedaling down the street. As he moves, he is making distance. His tire has a height of 1 foot and rotates around. The graphs axes are labled “position” and “time”. What function would model this situation?

Consider this…. The height of a geostationary satellite, which stays

over the same equatorial spot on the earth's surface as it orbits the planet in the direction of the earth's rotation. How high is the orbit? Too low, and the satellite must have a higher angular speed to apparently "travel eastbound"; too high, and it slips behind to apparently "travel westbound". (Away from the equator, and the component of gravity not needed for centripetal acceleration pulls the satellite toward the equator.) Assume a perfectly-spherical Earth that stays at a fixed point, with a satellite in a circular orbit at altitude "h", in whose plane the Equator lies

. R (radius of Earth) 6.37 x 106 meters

(angular speed of Earth) 7.2921 x 10-5 rad/sM

(mass of earth) 5.97 x 1024 kilogramG

(Gravitational Constant) 6.67259 x 10-11 m3*kg-1*s-

2

Search For….

An image that demonstrates the quadratic function.

Why did you choose this image?

Consider this…

The life span of an insect can be modified by the temperature of the environment. Assume that the relationship between temperature of the environment (in degrees Celsius) and lifespan of the fruit flies (in days) is linear. If a population of fruit flies has the life span of 80days at the temperature of 10 degrees and the life span of 50 days at the temperature of20 degrees, write the linear relationship between the temperature and the life span. Wha tis the life span at the temperature of 25 degrees? At what temperature is the life span 92 days?

Consider this….

A farmer has a spherical tank that he keeps the water for his cows in. He likes to keep the tank half-full and he usually checks the water level every 5 days. Sadly, he has fallen and injured himself and no one else knows how to check this. Luckily, there is a function that allows you to calculate the volume of water in a spherical tank. What function is it? Why?

Search for…

An image that demonstrates the Cubic function

Why did you choose this image?

Consider this….

A manufacturer sells a product for $8 per unit.  The fixed costs are $900 per month and the variable costs are $3.50 per unit. 

a)  How many units must be sold to break even? 

b)  Would a profit or loss occur if 1000 units are sold?

Consider this….

If your television monitor is a "21" inch monitor and its NOT a wide-screen, it means that the viewable area is diagonally 21 inches. You can then use the pythagorean therom to know that the vieable area has a width of about 22.4 inches wide by 16.8 inches high.

What function is used to obtain this data? Why?

Consider this…

suppose an economist consulted by a temporary employment agency indicates that the demand for temporary employment (measured in thousands of job applications per week) can be modeled by the function defined by

y = 4.3sin(0.82t + 0.3) + 7.3,where t is time in years since January 1998. We note that this function is a generalized sine curve and thus we can determine the amplitude as well as other information

Why is the sine wave the best to model this data?

Great Work!!!

There! You’ve looked at several ways that functions model real-life data and searched for images that look like particular functions! You are done with your unit on Functions!!