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# Algebra/algebra 2

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?

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

Questioner's Rating
 Rating(1-10) Knowledgeability = 10 Clarity of Response = 10 Politeness = 10 Comment Very wordy! Would have just liked the problem worked out.

Algebra

Volunteer

#### 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