Please help solve

Question

A toy rocket is shot vertically into the air from a 33 -foot-tall launching pad with an initial velocity of 104104 feet per second. Suppose the height of the rocket in feet t seconds after being launched can be modeled by the function h left parenthesis t right parenthesis equals negative 16 t squared plus v 0 t plus h 0h(t)=−16t2+v0t+h0 , where v 0v0 is the initial velocity of the rocket and h 0h0 is the initial height of the rocket. How long will it take for the rocket to reach its maximum height? What is the maximum height?

Answer 1

h(t) = -16t^2 + 104t + 33, per initial velocity and initial height

 

The max occurs at the Average of the zeros.

So first we need the zeros.

Since it cannot be factored, we use the quadratic formula.

 

-16t^2 + 104t + 33 = 0

 

16t^2 - 104t - 33 = 0

 

 [ 104 +or- sqrt ( 104^2 + 4(16)(33)) ]/ 32

 

As we are interested in the AVERAGE of the zeros,

the radical expression will cancel when the positive

and negative cases of the quadratic solutions are added.

 

The average is 208/64 = 3.25

At this time, the height is 202 feet

 

 

Calculus fans, read on....................................

 

 

 

 

 

 

 

 

The derivative is -32t + 104.

The max occurs when the derivative is zero.

That is 0 = -32t + 104

         -104/-32 = t

       t = 3.25