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

3 answers

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
In the first part where did you get the 93.5 from
Im not understanding the second part