i dont understand :(

Question

The height of a projectile fired upward is given by the formula s = v₀t − 16t²,

 where s is the height, v₀ is the initial velocity, and t is the time. Find the time for a projectile to return to Earth if it has an initial velocity of 232 ft/s.

Answer 1

h(t) = 232t -16t^2

take the derivative and set = 0

h'(t) = 232-32t = 0

t = 232/32 = 7.25 seconds to reach max height

multiply by 2

7.25x2 = 14.5 second to return to earth

or

set h(t) = 0 = 232t-16t^2

use the quadratic equation

t = 232/32 + sqr(232^2)/32 ignore the negative square root

t= 7.25 + 7.25 = 14.5 seconds to return to earth

ax^2 +bx + c = 0 is the standard form for a quadratic equation

-b/2a = time when it reaches maximum height

-b/a is when it reaches the ground when c=0

for -16t^2 + 232t = 0

a=-16, b=232 and -b/a = 232/16 = 14.5 seconds to reach the ground