The time the given ball traveled for is required.
The time the ball traveled was t = 3 seconds
Equation of motion
The given equation is [tex]H(t)=-16t^2+48t[/tex]
The ball never leaves the ground so the height of the ball is 0.
[tex]0=-16t^2+48t[/tex]
Solving the equation we get
[tex]-48t=-16t^2[/tex]
Dividing the equation by [tex]t[/tex] on both sides
[tex]\Rightarrow 48=16t[/tex]
Dividing the equation by 16 on both sides
[tex]\Rightarrow t=\dfrac{48}{16}\\\Rightarrow t=3\ \text{s}[/tex]
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