Nathan launches a water balloon vertically from a platform on his roof. The height of the balloon (in feet) is represented by the equation h=−16t2+28.7t+32.4, where t is the time (in seconds) after he launches the water balloon. What is the maximum height of the balloon?

45.27feet

Step-by-step explanation:

Given the height of the balloon (in feet) represented by the equation h=−16t2+28.7t+32.4, where t is the time (in seconds)

Note that the velocity of the balloon at maximum height is zero, hence;

v = dh/dt =0

-32t+28.7 = 0

-32t = -28.7

t = 28.7/32

t = 0.897secs

Get the maximum height

Recall that h=−16t²+28.7t+32.4

h = -16(0.897)²+28.7(0.897)+32.4

h= -12.87+25.74+32.4

h = 45.27feet

Hence the maximum height reached is 45.27feet