Algebraically determine the max height the snowball reaches

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Discussion Overview

The discussion revolves around determining the maximum height reached by a snowball thrown into the air, modeled by the quadratic function h = -4.9t² + 20t + 1.8. Participants are exploring algebraic methods to find the maximum height and the time the snowball is in the air, with a focus on whether calculus is necessary for the solution.

Discussion Character

  • Homework-related
  • Mathematical reasoning

Main Points Raised

  • One participant asks for help in determining the maximum height and mentions a method for finding the time the snowball is in the air.
  • Another participant suggests that the maximum height occurs when the velocity is zero, indicating that the derivative of the height function relates to this point.
  • A different participant questions whether the original poster has studied calculus, implying that calculus may be relevant to the problem.
  • Another response notes that the height function is a quadratic and suggests completing the square to find the vertex, which represents the maximum height, without the need for calculus.

Areas of Agreement / Disagreement

Participants have not reached a consensus on the necessity of calculus for solving the problem. Some suggest algebraic methods while others imply calculus might be needed.

Contextual Notes

There is an assumption that the original poster may not have knowledge of calculus, which could affect the approach to solving the problem. The discussion also reflects varying levels of familiarity with mathematical concepts such as derivatives and vertex form of quadratics.

Who May Find This Useful

Students seeking assistance with quadratic functions, maximum height problems, or those interested in the application of calculus in physics-related scenarios.

lauren
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my teacher gave me this q:
a snowball if thrown into the air. The function h= -4.9t^2 + 20t + 1.8 expresses the relationship between height, h, in meters and time, t, in seconds.
a) algebraically determine the max height the snowball reaches
b) how long is the snowball in the air?

i know to solve b you just need to plug in your h and solve for t. however for part a, i am not sure how to solve the max. can someone help?
 
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Do you have an equation for the velocity of the projectile as a function of time?

If not, do you know that velocity is the derivative of position with respect to time?

In either case, note that the ball reaches its maximum height when the velocity is zero.
 
no, all the info i got to solve this q i posted
 
Have you studied calculus?
 
lauren said:
my teacher gave me this q:
a snowball if thrown into the air. The function h= -4.9t^2 + 20t + 1.8 expresses the relationship between height, h, in meters and time, t, in seconds.
a) algebraically determine the max height the snowball reaches
b) how long is the snowball in the air?

i know to solve b you just need to plug in your h and solve for t. however for part a, i am not sure how to solve the max. can someone help?

h= -4.9t2+ 20t+ 1.8 is a quadratic. Its graph is a parabola with vertex at the top. Complete the square to find the vertex. You don't need to use calculus.
 

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