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AveGali [126]
1 year ago
6

I needs help with it ​

Mathematics
1 answer:
Slav-nsk [51]1 year ago
6 0

Answer:

a)  initial height = 0 m

b)  8 s

c)  vertex = (4, 32)

    maximum height = 32 m

Step-by-step explanation:

<u>Given equation</u>:

h=-2t^2+16t

where:

  • h is the height of the arrow about the ground (in metres)
  • t is the time (in seconds)

<h3><u>Part (a)</u></h3>

The initial height of the arrow will be at the beginning of its journey, so when t = 0

Substitute t = 0 into the equation and solve for h:

\implies h=-2(0)^2+16(0)

\implies h=0

Therefore, the initial height of the arrow is 0 m.

<h3><u>Part (b)</u></h3>

The arrow will hit the ground when the height is 0 m.

Substitute h = 0 into the given equation:

\implies -2t^2+16t=0

Factor out -2t:

\implies -2t(t-8)=0

Therefore:

\implies -2t=0 \implies t=0

And:

\implies t-8=0 \implies t=8

Therefore, the arrow will hit the ground at 8 seconds.

<h3><u>Part (c)</u></h3>

The vertex is the <u>turning point</u> of a parabola - it's minimum or maximum point.

As the leading coefficient for the given equation is <u>negative</u>, the parabola <u>opens downwards</u> and so its <u>vertex</u> is its <u>maximum point</u>.

There are different ways to find the vertex of a parabola. The easiest way to find the x-coordinate is by calculating the midpoint of the x-intercepts.

We have determined that the arrow has a height of 0 m at 0 seconds and 8 seconds.  Therefore, t = 0 and t = 8 are the x-intercepts.  The midpoint is halfway between zero and 8, so the midpoint is t = 4

To find the y-coordinate, substitute t = 4 into the equation and solve for h:

\implies h=-2(4)^2+16(4)

\implies h=-32+64

\implies h=32

Therefore, the coordinates of the vertex are (4, 32)

The maximum height is the y-coordinate of the vertex.

Therefore, the maximum height is 32 m

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