When will the stone reach its highest elevation and hit the ground?

[TbbZz]

Homework Statement

Suppose that an object is thrown into the air with an initial upward velocity of Vo meters per second from a height of ho meters above the ground.

Homework Equations

Then, t seconds later, its height (h(t) meters above the ground is modeled by the function h(t) = -4.9t^2 + volt + ho.

The Attempt at a Solution

a) Find its height above the ground t seconds later.

I got h(t) = -4.9t^2 + 14t + 30, and I checked the back of the book and it is correct.

b) When will the stone reach its highest elevation?

I tried a lot of things like plugging in various h's and t's, and using the quadratic formula, but I did not have much success.

c) When will the stone hit the ground?

Same as b), I wasn't sure where to start, but I made some educated guesses, however they proved wrong.

NOTE: I have all of the correct answers. I am not asking for anyone to do my homework for me or give me the answers. I would just like to be guided in the right direction so I will never have to ask for help on these types of problems again. I have worked for 20 minutes straight on this problem, and I know for a fact it shouldn't take that long.

Thank you for your time.

 

[rock.freak667]

Well if $$h(t) = -4.9t^2 + 14t + 30$$ doesn't this represent a parabolic curve? doesn't this curve have a maximum point...which would correspond to the max height and the time it occurs

 

[TbbZz]

Yes.

How do you find the maximum value of the parabolic curve, though?

 

[rock.freak667]

Find the the first derivative and equate to zero and solve for t

 

[TbbZz]

Find the the first derivative and equate to zero and solve for t

Would you mind clarifying what you mean by "the first derivative?" I don't quite understand what you mean. Thanks.

 

[HallsofIvy]

You will meet the derivative in Calculus and can use it to solve more comples problems. Here, because this is a quadratic, you can find the vertex of the graph by completing the square. That will give you the highest point.

 

[TbbZz]

Thanks for the assistance!