The Height The Height EquationEquation

• h= ending height• g = gravity constant (32 if feet,

9.8 if meters)

• v0= initial velocity

• h0 = initial height

• t = time

20 0

1

2h gt v t h

Example 1Example 1• Find the maximum height of an

object shot upward from the earth’s surface with an initial velocity of 106 ft/sec

SolutionSolution• Step 1 – Write the equation

• h = -16t2 + 106t + 0

• Step 2 – put it in your calculator, go to y = , put it in changing t’s to x’s.

• y = -16x2 +106x

• Step 3 – Graph by pushing zoom fit (zoom 0) zoom in or out until you get a good picture of the parabola

• Step 4 – Find the maximum. This is an ordered pair. The x is time and the y is height – this is always true!!

• Your solution is the x coordinate of the max.• 175.56 seconds

Example 2Example 2• A ball is thrown vertically

upward at an initial speed of 48 ft/sec from the top of a building 2000 feet high. How high does the ball go?

SolutionSolution• Step 1 –

• h = -16t2 + 48t + 2000

• Step 2 – graph it!!• Step 3 – Find the max• Step 4 – the answer is the y-

coordinate of the max.• 2036 feet

Example 3Example 3• A ball is thrown straight up with

an initial velocity of 56 ft/sec. The height of the ball in seconds after it is thrown is given by what equation? What is the maximum height of the ball? What is the height of the ball after 1 second? After how many seconds will the ball return to the ground?

SolutionSolution• Equation: h=-16t2 + 56t• Max Height: 49 feet• Height after 1 sec: 40 feet

• Explanation: to find the max height you should go to 2nd trace, value, then x = 1

• Time it takes to hit the ground: 3.5 sec• Explanation: to find when an object hits the ground

you are looking for the x-intercept (or zero) on the right hand side of your graph. You can find this by using the following steps:

» 1. Go back to y= and put 0 in the y2 equation. » 2. Hit graph» 3. Go to 2nd trace, intersection (5), move your cursor

over to the right hand x – intercept, then hit enter 3 times. You are looking for the x value.

Example 4Example 4• A ball is dropped

from the top of a 500 ft building with an initial velocity of 32ft/sec. How long does it take the ball to reach the ground?

• Answer: 6.68 seconds

• Explanation: Graph and find the right hand x - intercept. Need directions: go back to the last slide and follow the steps for “time it takes to hit the ground”.

Example 5Example 5• A ball is thrown

from the top of a tower at a velocity of 10 m/sec. The ball hit the ground at the base of the tower 4 seconds later. How high is the tower?

• Answer: 38.4 meters

• Explanation:2

0 0

20

0

20

0

0

0

0 4.9 10

now plug 4 in for t and solve for h

0 4.9(4) 10(4)

0 78.4 40

0 38.4

38.4

h gt v t h

t t h

h

h

h

h