SOLUTION: A rocket is scheduled to lift off from a stage 2ft. off the ground at an initial velocity of 80ft. per sec. How long is the rocket in the air? Use 32 ft/sec as the acceleration ra

Question 298365: A rocket is scheduled to lift off from a stage 2ft. off the ground at an initial velocity of 80ft. per sec. How long is the rocket in the air? Use 32 ft/sec as the acceleration rate of gravity(G). What will be the maximum height of the rocket? The converted formula for the height of an object propelled unto the air is h=-16t squared +vt+h sub zero... I think I have height as being 2ft, velocity is 80ft per sec h sub zero is 2ft? I'm so confused! Help! Please! Thank you, Natalie
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
A rocket is scheduled to lift off from a stage 2ft. off the ground at an initial velocity of 80ft. per sec. How long is the rocket in the air? Use 32 ft/sec as the acceleration rate of gravity(G). What will be the maximum height of the rocket? The converted formula for the height of an object propelled unto the air is h=-16t squared +vt+h sub zero
.
They give you the equation as:
h(t) = -16t squared + vt + "h sub zero"
where
h(t) is height
t is time
v is velocity
"h sub zero" is initial height
.
Given the data from the problem we now have:
h(t) = -16t^2 + 80t + 2
This is a parabola.
It opens downward (from the coefficient associated with the t^2 term).
So, finding the axis of symmetry gives you the peak.
"axis of symmetry" = -b/2a = -80/(2*(-16)) = -80/-32 = 2.5
So, when
t = 2.5 seconds
it will be at its peak.
.
To find the height, plug t back into:
h(t) = -16t^2 + 80t + 2
h(2.5) = -16(2.5)^2 + 80(2.5) + 2
h(2.5) = 102 feet

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