Expert: Richard J. Raridon - 2/28/2008

Question
Okay, so here is the question:

When an object suck as a bullet or a ball is shot or thrown upward with an initial velocity, its height is given by a quadratic function.

s(t)= -4.9tē+Vot+h

In this function, h is the starting height in meters, Vo is the velocity, s is the actual height (also in meters) and t is the time from projection in seconds.  This model is based on the assumption that there is no air resistance and that the force of gravity pulling the object earthward is constant.  Neither of these conditions exists precisely, so this model (as is the caSe with most mathematical models) gives only approximate results.  A model rocket is fired upward.  At the end of the burn, it has an upward velocity of 40m/second and is 155m high.  Find (a) its maximum height and when it is attained and (b) when the rocket reached the ground.

Hint: 1) Vertex will give max height.
     2) s(t) is 0 when rocket reaches ground

Please help, I have no idea what I'm doing.  D:

Answer
First of all you have to find out how long the rocket will continue upward.  For that you need V = Vo -gt.  0 = 40 -9.8t and t = 4.082s.  Now you can find the maximum height from the equation you listed. s(t) = -4.9(4.082)^2 +40(4.082) +155 = 236.6m
(b) 0 = -4.9t^2 +40t +155 and t = 11.0s