Quadratic equation

Question

Quadratic equations are used for many applications. The formula to solve quadratic equations can be used to solve all quadratic equations, even those that cannot be factored. A common application of quadratic equations is the height of a thrown object over time, which takes the earth's gravity and the velocity of the throw into account. For example, if someone throws a ball down from a height of 100 meters, the ball's distance from the ground can be modeled by the equation:  where t is the time in seconds and d is the distance in meters.

1. At what time (t) will the ball hit the ground? (Hint: what does this mean for d=distance?)
2. You will get two answers. Do both make sense? (Explain in detail Why or Why not).

Answer 1

The d (distance) basically indicates the position with regard to a reference. In this case, if t = 0, then d = 100 telling you that at the start, the ball is +100 units.

To find when the ball hits the ground (d = 0), you then have -9.8t2 - 15t + 100 = 0

Using the quadratic equation, you find that

t = 2.52 and -4.05

The answers are correct per the formula but in the real world, the negative number is not realistic.

So,

the ball hits the ground (reference = 0) at 2.52 seconds