Although quadratic equations are often used to find maximums and minimums for problems involving projectile motion, they can also be used to evaluate
the path of a projectile at various time periods. For example, quadratic equations can be used to determine the height
of a projectile at time “t” after the projectile has been released.
In order to work a problem involving quadratic evaluation at a point, it is necessary to
Suppose a ball is thrown directly upward from an initial height
of 200 feet with an initial velocity
of 96 feet per second. After how many seconds will the ball reach a height
of 300 feet?
We will begin by substituting our givens in to the projectile height
formula: At time t
= 0, vo
= 96 ft/sec, and so
= 200 feet.
of the equation
depicting the path of the ball is as follows:
We want to know what the value of t
will be when
= 300. To find out, we substitute 300 for
, and solve the quadratic equation
We have obtained two values that represent the time that the ball reaches a height
of 300 feet. The first value 1.
34 indicates that after 1.
34 seconds have passed, the ball is at a height
of 300 feet. Then the ball reaches its maximum height
and begins to fall back to the ground. After 4.
66 seconds it is once again at 300 feet. Then it will continue to fall to the ground. The answer we were seeking is 1.
34, the time the ball initially reached 300 feet after it has been thrown.