Casio fx-CG10 Advanced Operation Manual page 83

Chapter 6: Conic Sections
Investigation 6.1—Throwing High
Did You Know?
Terminal velocity is when a falling object stops accelerating. The net force of air
resistance and gravity is equal to zero. When the object reaches terminal velocity,
it will continue to fall but at a constant rate. If an object is more compact and
more dense, it has a greater terminal velocity. For example, the terminal velocity
of a raindrop is 25 feet per second, and the terminal velocity of a human is 250
feet per second.
Reference:
www.northallertoncoll.org.uk/physics/module%202/terminal%20velocity/terminal%20velocity.htm
When we ignore air resistance, the height of an object thrown vertically is a
quadratic function of the time it's been in the air. This is due to the downward
acceleration caused by gravity. We will let x represent time, measured in seconds,
and y represent height, measured in feet. The general form for this relationship is
2
y 16 x v x y . In this formula, y represents the initial height; v x is the linear
o o
0 0
component, where distance (in this case height) is the product of the initial velocity
2
in feet per second and time, measured in seconds; and 16x is the change in height
due to gravity. Gravity accelerates all objects, increasing their downward (thus the
negative) velocity by 32 feet per second every second. To have a sense of why the
coefficient is 16 and not 32, consider an object that is dropped from a given
height. Its initial speed is 0 feet per second, and after one second it will be falling at
32 feet per second. Because the acceleration is uniform, the average speed over
that second will be 16 feet per second.
Suppose a ball is thrown upward at a speed of 50 feet per second, and is released
from an initial height of 6 feet. The height of the ball, at any point in time, can be
2
modeled by the equation, y 16 x 50 x 6 . As suggested above, 16 represents
the downward acceleration due to Earth's gravity, 50 represents the initial vertical
speed with which the ball is thrown, and 6 represents the initial height of the ball
(Note: it's the height at time 0).