A model rocket is launched with an initial velocity of 11[c] feet per second fro

Question

A model rocket is launched with an initial velocity of 11[c] feet per second from the height of [a] feet. The function s ( t ) = ? 16 t 2 + 11 [ c ] t + [ a ] models the path of the rocket where t represents the time, in seconds, after which the rocket is launched and s represents the height of the rocket at time t. Fill in the table of values for the function, and give a short interpretation for each point. How long will it take for the rocket to return to the ground? How long will it take the rocket to reach its maximum height? What is the maximum height reached by the rocket?

Explanation / Answer

Solution : Taking [c] =7 and [a]= 2.

Thus the function become

s(t)=-16t^2+117t+2

When height s(t)=0, then -16t^2+117t+2=0

On solving for t, we get t =7.3296 seconds.

Thus to return to the ground it will take 7.3296 seconds.

And to reach its maximum height it will take 7.3296/2= 3.6648 second.

To find the maximum height putting t=3.6648 in the function, we get maximum height

s(t)=215.886 feet.

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