The Quadratic Formula |
A ball is tossed directly upward from a height of 2.0 m above the ground
with an initial velocity of 5.0 m/s. It is subject only to the force
of gravity while in flight, so it has an acceleration of
-9.8 m/s. When does the ball reach a height of 3.0 m? The position
of the ball as a function of time is given by the equation
Solution
The equation with the given information is
To understand the two solutions, a graph of the left side of Eq. 3 is helpful
If , then , and there is only one solution, . In the above example, this corresponds to 0.51 s, the time at which the ball reaches its maximum height.
If , then is imaginary (involves ). The above example does not have a physically reasonable solution corresponding to this situation. (This situation corresponds to heights never reached by the ball.)
Copyright © 2002-2004, Lewis A. Riley | Updated Mon Jan 19 13:29:10 2004 |