word problem

Question

Suppose that an air cannon in the Punkin Chunkin contest whose muzzle is
88
feet above the ground fires a pumpkin at an angle of
45 degrees45°
to the horizontal with a muzzle velocity of
391391
feet per second. The model
s left parenthesis t right parenthesis equals negative 16 t squared plus 296 t plus 8s(t)=−16t2+296t+8
can be used to estimate the height s of an object after t seconds.
(a) Determine the time at which the pumpkin is at a maximum height.

(b) Determine the maximum height of the pumpkin.

(c) After how long will the pumpkin strike the ground?

Answer 1

Hello Sterling Heights!  It's Saint Clair Shores calling!

 

use the vertex formula that will indicate the (x,y) point of the vertex.

 

(-b/2a, (f(-b/2a))  I hope you can look this up online or in your textbook.  NOte:  -16t^2+2906t+8 is a parabola that opens downward.  Therefore the vertex is a maximum, the highest point of the parabola.  

 

Good luck!