Gravity

Objects moving due to gravity can be described with quadratics. For objects near the surface of the earth the height of the object, h, can be predicted for any time t, given the initial height of the object, h_o, and the initial vertical velocity v_o. The value for the initial velocity is positive if the object is initially moving upward, negative if it is initially moving downward, and zero if the object is initially at rest. The equation that describes the motion is

h = g/2 t²+ v_ot + h_o

where g is -9.81 m/sec², the accepted value for earth's gravity.

a. If an object is dropped from a height of 20 meters with a zero initial velocity, use the above equation to determine how long it takes for the object to hit the ground. What is the maximum height of the object?

b. If instead of dropping the object we throw the object downward at 10 m/sec from a height of 20 meters, use the above equation to determine how long it takes for the object to hit the ground. What is the maximum height of the object?

c. If instead the object is thrown upward at 10 m/sec from a height of 20 meters, use the above equation to determine how long it takes for the object to hit the ground. What is the maximum height of the object? At what time does the maximum height occur?

d. Graph all three equations with time in seconds on the x-axis and height in meters on the y-axis. Indicate on your graphs the maximum heights and when the object hits the ground.