SOLUTION: A toy rocket is launched upward from ground level with an initial velocity of 39 meters per second. Its height is a function of time, given by h = -4.9t^2+39t, where h represents t

Question 631950: A toy rocket is launched upward from ground level with an initial velocity of 39 meters per second. Its height is a function of time, given by h = -4.9t^2+39t, where h represents the height in meters and t represents the time in seconds. What is the maximum height reached by the rocket and how long is it in flight?
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
A toy rocket is launched upward from ground level with an initial velocity of 39 meters per second. Its height is a function of time, given by h = -4.9t^2+39t, where h represents the height in meters and t represents the time in seconds. What is the maximum height reached by the rocket and how long is it in flight?
**
h = -4.9t^2+39t
complete the square:
h=-4.9(t^2-(39/4.9)t)
39/4.9≈7.96
(1/2*7.96)^2=3.98^2=15.84) (half the coefficient of t)^2
h=-4.9(t^2-7.96t+15.84)+77.62
h=-4.9(t-3.98)^2+77.62
This is an equation of a parabola that opens downwards so it has a maximum at the vertex.
Its standard form: y=(x-h)^2+k, (h,k)=(x,y) coordinates of the vertex.
For given problem:
Vertex: (3.98,77.62)
maximum height: 77.62 meters
flight time: 3.98 seconds
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