Mathematics, 23.08.2019 09:10 renee9913
Atoy 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 me
you in advance
Answers: 1
![h(t)=-16t^2+80t+5\\\\t_{max}-time\ for\ a\ maximum\ height\\\\t_{max}=- \frac{80}{2\cdot(-16)} = \frac{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.](/tpl/images/0190/5324/557d4.png)
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