A water balloon was launched into the top of the hill 38 feet above the ground

-71.104 ft/sec

Step-by-step explanation:So you need to know how fast the balloon is moving when it hits this person's head. velocity is based on time. So you need the time that it hits this person's head. You can get time from the position equation. Because the balloon hits this person's head 6 feet from the ground, you know that the final position is at 6 so you plug that into the position equation and solve for t. You look and see what the appropriate t value is and plug it into the velocity equation and see what the answer is.

6=-16t^2+40t+60

0=-16t^2+40t+54

plug in those values into the quadratic formula or your calculator and you get:

t = -.972

or

t = 3.472

since you can't have negative time, the other answer must be it.

So you then plug it in and solve.

v(3.472) = -32(3.472) + 40

which is approximately -71.104 ft/sec

or if they just want speed, 71.104 ft/sec. (remember, speed is velocity without direction)