Respuesta :
If the function of height in time is h(t)=-4.9[tex]t^{2}[/tex]+106t+206,then the rocket will splash down into the ocean after 23.43 seconds and the rocket will get its peak after 10.82 seconds at a height of 779.26524 meters above the sea level.
Given that the function of height in time is h(t)=-4.9[tex]t^{2}[/tex]+106t+206.
We are required to find the time after which the rocket will splash down into the ocean and the time after which the ocean will get its peak and the height of the rocket.
The rocket will splash down when the height of the rocket is 0.
-4.9[tex]t^{2}[/tex]+106t+206=0
4.9[tex]t^{2}[/tex]-106t-206=0
t={106±[tex]\sqrt{(106)^{2} -4*4.9*(-206)}[/tex]}/2*4.9
t=(106±[tex]\sqrt{15273.6}[/tex])/9.8
We have to ignore the negative sign because the time is always shown in positive signs.
t=(106+123.59)/9.8
t=229.59/9.8
t=23.43 seconds
Rocket will be at its peak when the slope of the equation is 0.
[tex]h^{I}[/tex](t)=-9.8t+106
-9.8t+106=0
-9.8t=-106
t=-106/-9.8
t=10.82 seconds
To find the height we need to use t=10.82 in the equation.
h(10.82)=[tex]-4.9*(10.82)^{2} +106*10.82+206[/tex]
=-573.65476+1353.92
=779.26524 meters.
Hence if the function of height in time is h(t)=-4.9[tex]t^{2}[/tex]+106t+206,then the rocket will splash down into the ocean after 23.43 seconds and the rocket will get its peak after 10.82 seconds at a height of 779.26524 meters above the sea level.
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