Question

Steve kicks a football into the air. The path that a ball takes can be described by the equation h=20t - 5t squared where h is the height of the ball in meters and t is time in seconds.
After how many seconds will the ball be 25 meters high?

Answer 1

Since h represents the height of the ball at any given time, t, let h = 25, such that the ball will be 25m high at t.

Now, we have 25 = 20t - 5t²
5t² - 20t + 25 = 0
t² - 4t + 5 = 0

$\frac{4 +- \sqrt{16 - 20}}{2}$

Since the discriminant is less than zero, there are no solutions.
Hence, the ball will never be 25m high.