Explanation:
It is given that,
Upward velocity of a boulder, v = 92 m/s
The height of the boulder, h, in meters after t seconds is given by the function as :
\(h=-5t^2+92t+16\)............(1)
We have to find the time taken by boulder to reach maximum height. For this, we have to differentiate equation (1) w.r.t. t and putting it equal to 0. So,
\(\dfrac{dh}{dt}=0\)
\(\dfrac{d(-5t^2+92t+16)}{dt}=0\)
\(-10t+92=0\)
t = 9.2 s
Putting the value of t = 9.2 s in equation (1). So,
\(h=-5\times (9.2)^2+92\times 9.2+16\)
h = 439.2 m
So, the time taken by it to reach maximum height is 9.2 s and the maximum height is 439.2 m. Hence, this is the required solution.
