Please help have an F in math

Question

Alice was sitting on a dock looking at a lake.SHe picked up a stone and through it in the air and out toward the lake.It seemed like it was in the air for a long time.The equation that can be used to model the height of the stone (in feet) as it relates to the time in the air (in seconds) s given by h(t)=5+50t-16t^2.In order to solve for how long the stone was in the air,Alice will need to use the quadratic equation

(-b±√(b²-4ac))/(2a)

How long was the stone in the air? round to the nearest hundredth if not an exact answer

Answer 1

h= -16t^2 + 50t + 5

set h=0, solve for t,

-16t^2 +50t + 5 = 0

t= -50/-32 + (1/32)sqr(50^2 +64(5)= about 3.222 seconds in the air = 3.2 rounded off to one decimal place

let t=3, h=-16(9)+150+5 = 11

let t=4 h= -16(16)+200+5 = -51

for h to =0, t has to be closer to 3 than to 4.

11/(11+51) = 11/62

3 +11/62= about 3.2

Answer 2

h(t) = -16t² + 50t + 5

When the stone hits the ground, its height is zero:

0 = -16t² + 50t + 5

Now use the quadratic formula to find the value of t.

t = (-b±√(b²-4ac)) /(2a)

For your equation, a = -16, b = 50, c = 5: Use your calculator to help. You'll get two answers, one positive and one negative. Since we haven't invented time travel yet, the positive answer is the one you want. The units are seconds.