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Sagot :
Answer:
(a)Yes
(b)5 seconds
Explanation:
Given the equation: h(t) = -3t² + 12t + 15
(a)To determine if the ball reaches a height of 16m, we find the maximum height of the cannon ball.
The maximum height occurs at the axis of symmetry.
First, we find the equation of symmetry.
[tex]\begin{gathered} t=-\frac{b}{2a} \\ =-\frac{12}{2\times-3} \\ =-\frac{12}{-6} \\ t=2 \end{gathered}[/tex]We find h(2).
[tex]\begin{gathered} h(2)=-3(2)^2+12(2)+15 \\ =-12+24+15 \\ =27\text{ meters} \end{gathered}[/tex]The ball reaches a height of 16 meters since its maximum height is 27 meters.
(b)The ball reaches the ground at the point when h(t)=0.
[tex]\begin{gathered} -3t^2+12t+15=0 \\ -3t^2+15t-3t+15=0 \\ -3t(t-5)-3(t-5)=0 \\ (t-5)(-3t-3)=0 \\ t-5=0\text{ or }-3t-3=0 \\ t=5\text{ or }-3t=3 \\ t=5\text{ or }t=-1 \end{gathered}[/tex]Since time cannot be negative, the ball hits the ground after 5 seconds.
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