First thing is I don't agree that this is thrown from the ground. At t=0, the position is 2. So I guess we can call 2 meters the origin. The rock will reach its max height at the vertex of this parabola. Have you taken Calculus?

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- Jun 1st 2006, 02:40 PM #1

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## Question!!!!!

heres the question

A rock is thrown vertically from the ground with a velocity of 24 meters per second and it reaches a height of 2+24t-4.9t(Squared) after t seconds. How many seconds after the rock is thrown will it reach maximum height and what is the maximum height the rock will reach in meters? how many seonds after the rock is thrown will it hit the ground? Round your answers to the nearest hundredth

Please help!!! I've tried everything and couldn't figure it out!!!

- Jun 1st 2006, 04:05 PM #2

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- Jun 1st 2006, 04:11 PM #3

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- Jun 1st 2006, 05:10 PM #4

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Hello, kkmarie9009!

A rock is thrown vertically from the ground with a velocity of 24 m/sec

and it reaches a height of after t seconds.

(a) How many seconds after the rock is thrown will it reach maximum height?

(b)What is the maximum height the rock will reach in meters?

(c) How many seconds after the rock is thrown will it hit the ground?

Round your answers to the nearest hundredth.

. . Its graph is a down-opening parabola.

. . The maximum height occurs at the vertex of the parabola.

The formula for the vertex of a parabola is:

Our parabola has:

The vertex is at:

(a) Therefore, the rock reaches maximum height at seconds.

If , then:

(b) Therefore, the maximum height is: m.

If the rock hits the ground, its height is zero.

. . Solve the quadratic:

Quadratic Formula:

Hence:

(c) Therefore, the rock hits the ground in about seconds.

- Jun 1st 2006, 05:26 PM #5

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- Jun 1st 2006, 06:52 PM #6
## The Quadratic Formula

Exactly why would you use the quadratic Formula?? is there an easier way to figure it out without it? or no?

Factoring:

Start with equation

Factor

Substitute 0 for "y"

or anything multiplied by 0 equals 0, so solve each factor for 0.

or Solve

Completing the Square:

Start with equation

subtract "c" from both sides

add to both sides

Factor

Find the square root of both sides

Solve square roots

or Solve each answer

or Solve