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]
