Answer:
0.75s , 15ft
Step-by-step explanation:
Use Derivatives,
Notice that the above function is a quadratic curve, meaning it has either a maximum or minimum point, which is the turning point and that is what we are solving for to find a 'max' or 'min'.
[tex]\frac{d}{dt}[/tex]h = [tex]\frac{d}{dt}[/tex](-16t² + 24t + 6)
[tex]\frac{dh}{dt}[/tex] = -32t + 24
At turning points (max/min),
the gradient is 0 meaning,
[tex]\frac{dh}{dt}[/tex] = -32t + 24 = 0.
t = 24/32 = 3/4
so time = 0.75 second
Substitute this t into the function,
we get h = -16 * 0.75 *0.75 + 24 * 0.75 + 6 = 15ft
