Question

In the past, professional baseball was played at the Astrodome in

Houston, Texas. The Astrodome has a maximum height of 63.4 m. The
height in meters of a baseball t seconds after it is hit straight up in the air
with a velocity of 45 m/s is given by h = -9.88 + 45t + 1. Will a baseball hit
straight up with this velocity hit the roof of the Astrodome? Use the
discriminant to explain your answer.

Answer 1

The correct value of the h function is; h= -9.8t² + 45t + 1

Answer:

Using the discriminant, no real solution exists and the baseball will not hit the roof.

Explanation:

We are told the height is expressed as;h= -9.8t² + 45t + 1

Also that the Astrodome has a maximum height of 63.4 m

Thus, to find out if the baseball hit at a velocity of 45 m/s will hit the roof, we'll replace h with 63.4m.

Thus;

63.4 = -9.8t² + 45t + 1

Subtract 63.4 from both sides to give;

-9.8t² + 45t + 1 - 63.4 = 0

-9.8t² + 45t - 62.4 = 0

Using quadratic formula, we have;

t = -45 ± √{(45² - (4 * (-9.8) * (-62.4)}

t = -45 ± √(2025 - 2446.08)

t = -45 ± √(-421.08)

The discriminant is -421.08

This value is less than 0.

Thus, no real solution exists and the baseball will not hit the roof.