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Question
Emilee and Charles shoot a rocket into the air during Mr. Jones' physics class at an initial velocity of 128 ft/sec. Use the equation of h = vt - 16(t squared) to find the maximum height, total time in the air, and how long it takes to land?

Answer
Assuming the 128 ft/sec is vertical (i.e. straight up), then...
h(t)=128t-16t^2 gives the equation of motion in the vertical direction
(i.e. the height above the ground).  Since this is a parabola, we know the
vertex (i.e. turning point) occurs on its axis of symmetry, t=-b/(2a)=-128/(2*(-16)) sec
==> t= -128/-32 sec = 4 sec.

Thus, h_max=128*4-16*4^2 ft = 512-256 ft = 256 ft, at t=4 sec.
It will hit the ground after another 4 sec. (when h=0 again after t=0),
hitting the ground after 8 sec.

OK?

A. Mantell

Algebra

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Abe Mantell

Expertise

Hello, I am a college professor of mathematics and regularly teach all levels from elementary mathematics through differential equations, and would be happy to assist anyone with such questions!

Experience

Over 15 years teaching at the college level.

Organizations
NCTM, NYSMATYC, AMATYC, MAA, NYSUT, AFT.

Education/Credentials
B.S. in Mathematics from Rensselaer Polytechnic Institute
M.S. (and A.B.D.) in Applied Mathematics from SUNY @ Stony Brook

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