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.
The
graph 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 for
t.
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.