looking for time interval (seconds) using interval notation

Question

Using calculus, it can be shown that if a ball is thrown upward with an initial velocity of 80 ft/s from the top of a building 252 ft high, then its height h above the ground t seconds later will be
h = 252 + 80t − 16t2.

Answer 1

Yes.  So what is your question?
h(t) = (-1/2)at² + v₀t + h₀
 
h(t) represents height at a specific time t
a = acceleration ... acceleration of gravity is 32 ft/s² or 9.8 m/s²
v₀ = initial velocity
h₀ = initial height
 
If we want to find out how long it would take to hit the ground,

which is a height of zero, then h(t) = 0, solve for t

 

-16t² + 80t + 252 = 0

factor out a 4

-4t² + 20t + 63 = 0

 

From quadratic equation:

t = [-20 ±√((20²-4(-4)(63))]/(2(-4))

 

Solve for t and discard any negative answer from

the roots