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

In summary, the conversation discusses finding the height, highest elevation, and time of impact for an object thrown into the air. The height is represented by the function h(t) = -4.9t^2 + Vot + ho and the highest point can be found by finding the first derivative and equating it to zero, or by completing the square. This can be used to find the time of impact and the maximum height.
  • #1
TbbZz
37
0

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 + Vot + 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.
 
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  • #2
Well if [tex]h(t) = -4.9t^2 + 14t + 30[/tex] 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
 
  • #3
Yes.

How do you find the maximum value of the parabolic curve, though?
 
  • #4
Find the the first derivative and equate to zero and solve for t
 
  • #5
rock.freak667 said:
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.
 
  • #6
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.
 
  • #7
Thanks for the assistance!
 

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

What is a quadratic function?

A quadratic function is a mathematical function that is defined by an equation of the form f(x) = ax^2 + bx + c, where a, b, and c are constants and x is the variable. The graph of a quadratic function is a parabola.

How do you solve a quadratic function?

To solve a quadratic function, you can use various methods such as factoring, completing the square, or using the quadratic formula. The goal is to find the values of x that make the equation true.

What is the vertex of a quadratic function?

The vertex of a quadratic function is the point on the graph where the parabola changes direction. It is also the highest or lowest point on the graph, depending on whether the parabola opens up or down. The coordinates of the vertex can be found using the formula (-b/2a, f(-b/2a)), where a and b are the coefficients of the quadratic equation.

How do you determine the domain and range of a quadratic function?

The domain of a quadratic function is all the possible values of x that make the function defined. It can be determined by looking at the graph and determining the left and right endpoints. The range of a quadratic function is all the possible values of y that the function can output. It can be determined by looking at the vertex and the direction in which the parabola opens.

How are quadratic functions used in real life?

Quadratic functions are commonly used in physics, engineering, and economics to model various real-life situations. For example, the trajectory of a ball thrown in the air can be modeled using a quadratic function. In business, quadratic functions can be used to determine the maximum profit or minimum cost for a given situation.

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