Question

A toy rocket is shot vertically into the air from a launching pad 5 feel above the ground with an initial velocity of 80 feet per second. The height h, in feet, of the rocket above the ground as t seconds after launch is given by the function h(t)=-16t^2+80t+5. How long will it take the rocket to reach its maximum height? What is the maximum height?

CAN ANYONE HELP ME ASAP!!!!
Thank you in advance

Answer 1

For this case we have the following function:

`image`

To find the time when it reaches its maximum height, what we must do is to derive the function.

We have then:

`image`

We set zero and clear the time:

`image`

`image`

Then, we evaluate the time obtained for the function of the height.

We have then:

`image`

Answer:

It will take the rocket to reach its maximum height:

`image`

the maximum height is:

`h (2.5) = 105 feet`

Answer 2

`h(t)=-16t^2+80t+5\\\\t_(max)-time\ for\ a\ maximum\ height\\\\t_(max)=- (80)/(2\cdot(-16)) = (80)/(32) =2.5\ [s]\\\\h_(max)-the\ maximum\ height\ above\ the\ ground\\\\h_(max)=h(2.5)=-16\cdot2.5^2+80\cdot2.5+5=-16\cdot6.25+200+5=\\.\ \ \ \ \ \ =-100+205=105\\\\h_(max\ rocket)-the\ maximum\ height\ of\ a\ toy\ rocket\\\\h_(max\ rocket)=105-5=100\ [ft]\\\\Ans.\ t_(max)=2.5\ second,\ \ h_(max\ rocket)=100\ feet.`