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Question 1166876: A toy rocket is shot vertically into the air from a launching pad 9 feet above the ground with an initial velocity of 64 feet per second. The height h, in feet, of the rocket above the ground at t seconds after launch is given by the function h(t)= -16t^+64t+9. How long will it take the rocket to reach its maximum height? What is the maximum height?
Answer by ikleyn(52775)   (Show Source):
You can put this solution on YOUR website! A toy rocket is shot vertically into the air from a launching pad 9 feet above the ground with an initial velocity
of 64 feet per second. The height h, in feet, of the rocket above the ground at t seconds after launch is given by the
function h(t)= -16t^+64t+9. How long will it take the rocket to reach its maximum height? What is the maximum height?
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The function H(t) = -16t^2 + 64t + 9 is a quadratic function, whose plot is a parabola opened down.
This quadratic function has the maximum at the value of its argument t =  , where "a" is the coefficient at t^2
and "b" is the coefficient at t.
In your case, a= -16, b= 64, so the function gets the maximum at t =  = 2 seconds.
So, the ball gets the maximum height 2 seconds after is hit straight up.
The maximum height is H(t) = -16*2^2 + 64*2 + 9 = 73 ft. ANSWER
Solved.
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On finding the maximum/minimum of a quadratic function, see the lessons
- HOW TO complete the square to find the minimum/maximum of a quadratic function
- Briefly on finding the minimum/maximum of a quadratic function
- HOW TO complete the square to find the vertex of a parabola
- Briefly on finding the vertex of a parabola
in this site.
On solving similar problems to yours in this post, see the lessons
- Problem on a projectile moving vertically up and down
- Problem on an arrow shot vertically upward
- Problem on a ball thrown vertically up from the top of a tower
- Problem on a toy rocket launched vertically up from a tall platform
in this site.
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