Algebra word problem

Question

The height of a leaf after it falls frm a tree to the ground is given by s(t)= -3.5t^2 + 37.8, where time is in seconds and the height is in feet above the ground. When would the leaf land on top of a person's head if the person was seated on the ground under the tree and their head was 2.9 feet above the ground?

Answer 1

Set s(t) = 2.9

 

Then, -3.5t²+37.8 = 2.9

 

                  -3.5t² = -34.9

 

                       t² = 9.9714

 

                       t = ±3.16

 

Since t > 0, t = 3.16 sec

 

 

Answer 2

Set  s(t)=2.9  because this would be the height of the leaf after it falls.  Next, solve for t from this equation.  But I think your equation might be incorrect.