Pls help I need these points Justin Launches a water balloon vertically from a platform on his roof height in feet is represented By the equation H = -16t^2+32t+48,where T is the time (in seconds) after he launch is the water balloon

What is the maximum height of the water balloon?

How long does it take to reach its maximum height?

Step-by-step explanation:

Given the height in feet represented by the equation H = -16t²+32t+48, at maximum height, the velocity of the water balloon is zero.

Velocity = dH/dt = 0

dH/dt = -32t+32 = 0

-32t+32 = 0

-32t = -32

t = -32/-32

t = 1sec

Substituting t = 1sec into the modeled equation of the height

H = -16t²+32t+48

H = -16(1)²+32(1)+48

H = -16+80

H = 64 feet

The maximum height of the water balloon is 64 feet

b) In order to know how long it takes to reach its maximum height, we will substitute H = 64 feet into the equation of the height.

64 = -16t²+32t+48

-16t²+32t = 16

16t²-32t+16 = 0

t²-2t+1 = 0

t²-t-t+1 = 0

t(t-1)-1(t-1) = 0

(t-1)² = 0

t-1 = 0

t = 1sec

It took the water balloon 1 sec to reach its maximum height.

step-by-step explanation: