How high can you throw a ball on another planet?

(Graphing Calculators)

HSCE: A3.3.1: Write the symbolic form and sketch the graph of a quadratic function given appropriate information.

The equation h = ½ gt2 + vt + s describes the vertical component of the ball if you were throwing it straight up in the air.

h = height of the ball at any given time in meters

g= acceleration due to gravity (-9.81 m/s2 on earth)

v = initial velocity you threw the ball with (meters per second)

s = starting height off the ground from where you threw the ball (in meters)

t = time in seconds

h = ½ gt2 + vt + s

on earth the gravity(g) = -9.81 m/s2

Use your graphing calculator to graph the equation: h = ½ gt2 + vt + s

for the following problem:

A ball was thrown with an initial velocity of 10 m/s with a starting height of 1 meter.

Rewrite the equation with the information given in the problem:

h =

Enter the equation in the y= screen of your calculator

Graph the equation

Adjust the window screen to Xmin=

Xmax=

Ymin=

Ymax=

Draw a sketch of the graph at the right:

What is the independent variable?

What is the dependent variable?

Use the trace key to find out the maximum height of the ball?

After how many seconds has the ball reached its highest point?

Let’s find how high you can throw a baseball:

Use the equation:

h = ½ gt2 + vt + s

In order to find how high you can throw a ball, we need:

1. how fast you can throw the baseball (velocity v)

2. at what height you started at (initial height s)

3. the gravity (g) of the planet you are on

Let’s collect some data!

  1. Record the speed you can throw a baseball: ______miles per hour

1b. Convert the speed to meters per second: multiply by 0.4470:

______meters per second (v)

  1. Measure the height you started your throw from the ground in meters:

______meters(s)

  1. The gravity on earth is -9.81 m/s2 (g)
  1. Fill in these values in your equation: h = ½ gt2 + vt + s

h = ______

  1. Graph your equation on your graphing calculator, adjust your window and make a sketch on your graph paper.
  1. Use the trace key to find the maximum height you can throw the ball on

earth.______meters

How many seconds did it take to get to this height? ______sec

How high can you throw a baseball on another planet?

Use your gravity chart for a different planet to change g in your equation. Write your new equation.

Planet: ______equation: h = ______

Graph your new equation. Make a sketch of your graph on your graph paper in a different color. Label it.

How high can you throw a baseball on your planet? ______

Try 2 other planets, sketch their graphs on the graph paper in different colors:

Planet: ______h = ______maximum height: ______

Planet: ______h = ______maximum height: ______

Hmmm…

  1. Explain how to use the graph and trace to figure out how long the baseball is in the air each time.
  1. How is number 1 related to using factoring to solve a quadratic equation?
  1. What are some errors we might find in this exploration?

Extension: NASA launched a probe that would land on several planets, including Mercury, Mars, Saturn, Jupiter, and Neptune. The probe launched baseballs into the air on each planet with an initial velocity of 41.57m/s at a starting height of 1.33m. The data collected was sent to Mission Control. Since the signal was distorted due to solar flares, only one item per planet was sent. Match the time/height information to the planet it corresponds to. (You will not be able to match all 5 planets.)

h = ½(-25.95)t2 + 41.57t + 1.33

x time / y height
-0.03 / 0
0.42 / 15.91
0.82 / 30.67
2.95 / 62.74
5.09 / 30.67
5.53 / 15.91
5.94 / 0
  1. Neptune
  2. Saturn
  3. Mercury
  4. Mars
  5. Jupiter

1. On which planet was the ball thrown the highest? Explain.

2. On which planet was the baseball in the air the longest? Explain.