Question 150020
# 13


In order to find the time it takes to reach the max height, use this formula:


{{{t=(-b)/(2a)}}} Start with the given formula.



From {{{y=-16t^2+96t+40}}}, we can see that {{{a=-16}}}, {{{b=96}}}, and {{{c=40}}}.



{{{t=(-(96))/(2(-16))}}} Plug in {{{a=-16}}} and {{{b=96}}}.



{{{t=(-96)/(-32)}}} Multiply 2 and {{{-16}}} to get {{{-32}}}.



{{{t=3}}} Divide.



So it takes 3 seconds for the projectile to attain its maximum height.


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ii)


To find the max height, simply plug the time {{{t=3}}} into the equation {{{y=-16t^2+96t+40}}}




{{{y=-16t^2+96t+40}}} Start with the given equation.



{{{y=-16(3)^2+96(3)+40}}} Plug in {{{t=3}}}.



{{{y=-16(9)+96(3)+40}}} Square {{{3}}} to get {{{9}}}.



{{{y=-144+96(3)+40}}} Multiply {{{-16}}} and {{{9}}} to get {{{-144}}}.



{{{y=-144+288+40}}} Multiply {{{96}}} and {{{3}}} to get {{{288}}}.



{{{y=184}}} Combine like terms.



So the max height is 184 feet.