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 , from a starting height of , the function describing its height after t seconds is . 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:
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 = whatever height you threw it from), and figure out the speed you threw it upward ( ).
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?
