Respuesta :
Given the equation:
[tex]h=-16t^2+60t[/tex]Let's find the time it takes the ball to return to the ground.
When the ball returns to the ground, the height, = 0.
Hence, to find the time it takes the ball to return to the ground, substitute 0 for h and solve for t:
[tex]0=-16t^2+60t[/tex]Solving further:
Re-arrange the equation
[tex]-16t^2+60t=0[/tex]Factor out -4t:
[tex]-4t(4t-15t)=0[/tex]We have the individual factors:
[tex]\begin{gathered} -4t=0 \\ and \\ 4t-15=0 \end{gathered}[/tex]Solve each equation for t:
[tex]\begin{gathered} -4t=0 \\ Divide\text{ both sides by -4:} \\ \frac{-4t}{-4}=\frac{0}{-4} \\ \\ t=0 \end{gathered}[/tex]For the second factor:
[tex]\begin{gathered} 4t-15=0 \\ Add\text{ 15 to both sides:} \\ 4t-15+15=0+15 \\ 4t=15 \\ \\ Divide\text{ both sides by 4:} \\ \frac{4t}{4}=\frac{15}{4} \\ \\ t=3.75 \end{gathered}[/tex]Therefore it will take 3.75 seconds for the ball to return to the ground.
ANSWER:
3.75 seconds
