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The height, h metres, of a springboard diver above the surface of the water t seconds after she leaves the board is given by h=-5t-12+7. Find the maximum height reached by the diver? How long does it take for the diver to reach maximum height? Find the height of the diving board?

Sagot :

MrRoyalidn

Answer:

[tex]h_{max} = 14.2m[/tex]

[tex]t = 1.2[/tex]

The height of the diver is 7m

Step-by-step explanation:

Given

[tex]h(t) =-5t^2 + 12t + 7[/tex]

Solving (a): The maximum height reached

First, we calculate the time to reach the maximum height using:

[tex]t = - \frac{b}{2a}[/tex] --- maximum of a function

Where

[tex]a = -5; b = 12; c = 7[/tex]

So, we have:

[tex]t = -\frac{12}{-2 * 5}[/tex]

[tex]t = \frac{12}{10}[/tex]

[tex]t = 1.2[/tex]

So, the maximum height is:

[tex]h(t) =-5t^2 + 12t + 7[/tex]

[tex]h(1.2)=-5 * 1.2^2 + 12 * 1.2 + 7[/tex]

[tex]h(1.2)=14.2[/tex]

Hence:

[tex]h_{max} = 14.2m[/tex]

Solving (b): Time to reach maximum height

This has been calculated in (a)

[tex]t = 1.2[/tex]

Solving (c): Height of the board.

This can be calculated by setting [tex]t =0[/tex] --- i.e. the height of the diver before diving

So, we have:

[tex]h(t) =-5t^2 + 12t + 7[/tex]

[tex]h(0) = -5 * 0^2 + 12 * 0 + 7[/tex]

[tex]h(0) = 7[/tex]

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