If an object is dropped from a height of 38 feet the function of each equals -16 what’s that mean T2 +38 gives the height of an object after two seconds how lon

Question

H=-16t2 +38.  How long does it take the object to reach the ground 

Answer 1

The wording of the question is unclear, but it looks like you want to find the height of the object after it has fallen 2 seconds, and you want to find how long it takes to reach the ground.

 

If dropped from rest,

 

h(t) = -16t² + 38,

 

with t in seconds and h in feet.

 

h(2) = [-16(2)² + 38] ft = ? ft

 

If you want to find how long it takes to reach the ground, set h(t) = 0 and solve for t.

 

-16t² + 38 = 0 ⇒

 

t = √(38/16) s = ? s

Answer 2

Your question was a little unclear, but I'll give it a shot.

If the equation for the height of an object at time, t, is given by H=-16t2 +38, then we can find its height at any time.

 

The point at which the object hits the ground will be when H=0

0=-16t²+38

-38=-16t²

-38/-16 = t²

19/8 = t²

√(19/8) = t

t≅ 1.54 sec.