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Calculus/velocity, speed word problem

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Expert: Alon Mandes - 11/8/2008


Question
1) A ball thrown vertically upward at t=0 seconds has an initial velocity of 96ft/sec and initial height of 112ft.

a)  what is the max height obtained by the ball?

b) What is the velocity of the ball when it has reached its max height coming down?

c) At what time does the ball hit the ground?

d) What is the speed of the ball when it hits the ground?

Thanks for your help, hope you can help me.

Answer
Suppose that g=32 ft/s^2. So :
a) let's calculate 1st the time till the ball reaches it's max height
v=vo-gt -> 0=96-32t -> t=3 sec.
h=vot-gt^2/2 -> h=96*3-32*9/2=144 ft
Max H = 144+112 = 256
c) + d)
mgh=mv^2/2 -> v=sqrt[2gH]=128 ft/s ("This is the velocity where the
ball hits the ground")
Let's calculate time :
v=vot-gt -> 128=0-32t -> t=4 sec.

Alon.

Calculus

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Alon Mandes

Expertise

Kind of questions I can answer : Limits, Derivatives, Integration, Implicit functions, continuousity, differentiation ,Extremum problems, Lagrange multipliers, Gradients, Surface integrals, Multi variables functions ,Multi variables Integrals,Complex variables ,Complex functions, Curves, Trajectory integrals & Vector analyse,Divergence,Rotor & word problems. Kind of question I can't answer : Economics,Combinatorics,infinite series & convergence ,Statistics & Probabilities .

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1. I'm a team member of mathnerds (math site for answering questions) 2. I'm a team member in the Student's Union of the Technion, helping students who have problems in mathematics. 3. 2 years of experience as a math teacher in college. 4. I give free homework help for high school students in Mathematics & Physics. 5. I teach part time in collage the subjects : "Digital Signal Processing" , "Random Signals & Noise" , "Complex Functions".

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Hi-Tech company : GSM4VOIP ; job possition : Algorythm developer.

Education/Credentials
M.A in Mathematics & Bs.c in Electronics.

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