Applications Day 1

Do Now1) Find a quadratic equation to best model the

data below using your graphing calculator. Use your equation to answer the question.

That’s Money Origami…Morigami?

What’s Going on This Week?

Monday-Applications

Tuesday-Applications Mini-Presentations

Wednesday-Applications Performance Assessment

Thursday-Chapter 5 Review Game, Review Sheet Due

Friday-Chapter 5 Test

By definition, a projectile has a single force that acts upon it - the force of gravity. If there were any other force acting upon an object, then that object would not be a projectile.

Yes, please memorize the formulas……

ExampleA ball is thrown directly upward from an initial height of 200 feet with an initial velocity of 96 feet per second. After how many seconds will the ball reach its maximum height? And, what is the maximum height?

SolutionLet's begin by substituting known values for

variables in the formula:

h(t)=-16t2+96t+200

Finding the time to reach its max height (the x-value of the vertex):

t=-b/2a=-96/(2*-16)=3 seconds

Plug t=3 into the equation to get the maximum height of 344 feet.

Graph

When is it 300 feet off the ground?

Solve

On the calculator, we get (rounded to the nearest hundredth), t=1.34 seconds and t=4.66 seconds. This makes sense. Sometimes you will get a negative time, in which case you will reject it. In this case, there are two possibilities (on its way up and on its way down).

If I wanted to find where it was at 100 feet, I would get t=-.91 seconds and t=6.91 seconds. I could reject the negative time.

More Examples! Suppose a ball is tossed up with an initial velocity of 45 feet per second. Say I’m 6 feet tall, so initial height is 6 feet. What would the equation be? How long will the ball stay in the air? If the initial velocity increases, will the ball stay in the air longer or shorter?

Problem with no velocity

A parrot dropped a piece of an apple while sitting at the top of a 20 meter high tree. Make an equation describing the height at t seconds. How long will it take the piece of apple to reach the ground? Check your work on the graphing calculator.

A soccer ball resting on the ground is kicked with an upward velocity of 48 ft/sec. Write a vertical motion equation. What is the greatest height of the ball and at what time will it be reached? How many seconds after being kicked will the ball reach the ground? Check your work on the graphing calculator.

A diver jumps down from a ledge which is 48 feet above the ocean at a rate of 8 feet per second. Write a vertical motion model. (Equation). How long will it take until the diver hits the water? Check your work on the graphing calculator.

Jim is standing at the edge of a 3000 foot deep canyon. He kicks a ball into the air with an initial velocity of 32 ft./sec. What is the greatest height above the canyon’s edge that the ball will reach? How long will it have traveled when it reaches this height? When will the ball return to the height it was kicked? When will the ball hit the canyon floor? ***Hint*** Let the edge represent initial height of 0 instead of 3000 and canyon floor represent -3000. Check your work on the graphing calculator.