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Question

A ball is thrown vertically upward from the ground with an initial velocity of 56 feet per second. For how many seconds will the ball be going upward? Assume the acceleration due to gravity is a(t) = -32 ft/sec^2

Answer 1

Thats a doozie, try this site http://www.mathway.com/

Answer 2

Working formula is

Vf - Vo = gT

where

Vf = final velocity = 0 (at its peak)

Vo = initial velocity = 56 given

g = acceleration due to gravity = -32 ft/sec^2

T = time for object to reach its peak

Substituting values,

0 - 56 = (-32)T

Solving for T,

T = 56/32

T = 1.75 sec.  

Answer 3

You just need to know (and understand) these three simple formulas. My teacher calls them "orange mirror" equation...

vf=final velocity

v0= initial velocity

delta x= change in x (distance)

ax=acceleration(its actually a sub x)

t= time

So...

vf=vo+ axt

delta x= vot+.5axt

vf^2=vo^2+ 2ax(delta x)

I would give you the derivations...but I don't remember what's the first step and don't want to get my other physics notebook...so these equations look kind of intimidating in this computer format but they are actually pretty simple.

You have initial velocity or vo= 56ft per second

You have acceleration a= -32 ft/sec^2

And you are looking for time.

So which equation has what we need? the first one...you might be asking what vf is...and since the ball goes up, it's velocity at the end (it's apex) is going to be zero.

Using the first equation

0=56-32t

and you can solve the rest of the equation for t..

Answer 4

v = a * t

the time it takes a ball starting at 56 fps to reach zero (falling back to earth) is the same as a ball starting at zero and accelerating (via gravity) to 56.fps.

56ft/sec = (32ft/sec^2) * t sec

all the units cancel out (a good sign) and you're left with:

t = 56/32 = 1.75 sec

Answer 5

Ok, we need to solve for Time = t, using acceleration=a and initial velocity. HOW CAN WE FIND THESE THREE VARIABLES IN ONE EQUATION???!!

ok.  Take this from a physics major.  So there is a master equation that you can use for ALL of these. Every motion problem for the rest of your physics life can come from this one equation: It is :

x(t) = Xo + Vo*t + 1/2*a*t^2

From this, you can derive all the others.  So let's take first derivative and see what happens:

dx(t)/dt = v(t) = Vo + a*t   (which is a nice convenient relationship between all three variables as mentioned before... so whee heww, solve for t!)

t =  ( V(t) - Vo )  / a

the velocity at t will equal 0, since that is when the ball is in rest in the air, the point at which it is not moving upward anymore and beginning to move downard.  The Vo is the initial velocity from the equation, the speed at which we threw the ball upward.  a is the acceleration due to whatever force is affecting it, in this case, it's gravity.  

(0- 56 ) / - 32   = You solved it!