Step 1:
Write the function
[tex]\text{h(x) = -16x}^2\text{ + 48x + 6}[/tex]Step 2:
When does the ball reach its maximum height? mean you should calculate the time taken for the ball to reach maximum height.
The ball reach maximum height at v = 0, when velocity = 0 m/s
Step 3:
[tex]\begin{gathered} h(x)=-16x^2\text{ + 48x + 6} \\ v\text{ = -32x + 48} \\ -32x\text{ + 48 = 0} \\ 32x\text{ = 48} \\ x\text{ = }\frac{48}{32} \\ \text{ x = }\frac{6}{4} \\ \text{x = }\frac{3}{2}\text{ = 1.5 seconds} \end{gathered}[/tex]a) the ball reaches its maximum height at x = 1.5 seconds
b)
maximum height reach at x = 1.5 seconds
[tex]\begin{gathered} m\text{aximum height} \\ =-16(1.5)^2\text{ + 48(1.5) + 6} \\ =\text{ -36 + 72 + 6} \\ =\text{ 42} \\ \end{gathered}[/tex]The maximum height of the ball is 42m
c)
the time that will pass in seconds from the start of the shot to the ball hitting the floor = 2 x 1.5
= 3 seconds
