Question

An astronaut on the moon throws a baseball upward. The astronaut is 6 fee, 6 inches tall and the initial velocity of the ball is 30 feet per second. The height of the ball is approximated by the function
s(t)= -2.7t^2 + 30t + 6.5

The ball will never reach a height of 100 feet. How can this be determined analytically?

After how many seconds is the ball 12 feet above the moon’s surface?

I need help starting off with both

Answer 1

first part:
replace s(t) with 100
100 = -2.7t^2 + 30t + 6.5
2.7t^2 - 30t + 93.5 = 0
This quadratic has no real solution, the discriminant
b^2 - 4ac or (30^2 - 4(2.7)(93.5) is negative.

So it can never reach 100

Does it reach 12 ??
Repeat the above by replacing s(t) with 12
I would use the quadratic equation and use the positive result to find the value of t, the time this happens

Answer 2

In the first part where did you get the 93.5 from

Answer 3

Im not understanding the second part