Algebra 2 with Trigonometry Mr. Yates

Name ______Date ______Algebra 2 with Trigonometry Mr. Yates

When a ball is thrown through the air, or a person skydives from a plane, quadratic functions (and parabolas) describe their motions. Gravity causes items to fall at an acceleration rate of 32 feet per second per second, equal to 9.8 meters per second per second. This is called the gravitational constant g.

If you throw something up in the air at an initial upward velocity of v0 , from a starting height h h   1 gt 2  v t  h of 0 , the function describing its height after t seconds is 2 0 0 . For example, a ball dropped from a building that is 50m tall has equation:

You can evaluate this function at any time to find out how high the ball is above the ground. For example, h(2 seconds) =

A height of zero indicates the ball is at the ground; a height less than zero would occur in your equation once the ball has already landed. Let’s solve the quadratic equation to find out when the ball hits the ground:

Be careful which g to use, depending on the units: feet or meters. On a separate sheet of paper, show work setting up an equation, then solve using the quadratic formula. 1. A) What is the height after three seconds of a penny dropped from the roof of the empire state building in New York City (1250 feet tall)? B) What is the height after four seconds? C) After how many seconds does the penny hit the ground? 2. A) What is the height after one second of a basketball thrown up into the air from a height of six feet, with an initial speed of 20 feet per second? B) After how many seconds does the basketball hit the ground? 3. A) What is the height after three seconds of an algebra textbook thrown from the roof of the Legg Mason building in Baltimore (151m tall), if it is thrown upwards with an initial velocity of 10m/s? B) After how many seconds does the algebra textbook hit the ground? 4. A) Throw a block up and time how long it takes to hit the ground (make sure it doesn’t hit the ceiling, or else the equation will be off). So h = 0 when t = ?

B) Substitute these values of h and t into the gravity equation (with h0 = whatever height

you threw it from), and figure out the speed you threw it upward ( v0 ). C) State your resulting function here: D) Sketch or print its graph (make sure you zoom to see a good picture). E) What was the height of the block after 1 second? 5. Make up a word problem involving gravity, then set up an equation (explaining where it comes from) and solve your word problem.