Suppose you were given the maximum height of an object and an equation that described its arc through the air. Is it possible introduce time as a parameter using gravity?

Question

akashdeepdeb · Answer

I don't think so, the parabola equation does not really contain 't' in it.

anonymous · Answer

Thats what I thought. The worksheets for this class are notoriously bad, but I wanted to check. The wording is "In order to introduce the parameter of TIME t into this situation, first find the time it takes the ball to fall to the ground from its maximum height. Then find the balls speed when it hits the ground. "

anonymous · Answer

Now, It would be easy to say that the max height is 90feet, gravity is -32.17ft/s^2 etc... but that doesnt apply to the balls arc, only its straightline distance downward...

akashdeepdeb · Answer

See if the parabola/arc equation is given.
It is actually derived from equating time into the equation.
Now if you know the initial velocity which I think you can derive. 

You can get a quadratic equation with time as you already have height.

And this all should be done in the y-axis.

anonymous · Answer

the parabola is -.00826(x-330)^2+90

anonymous · Answer

I dont see any way to determine its velocity at any point. Yes at 90 feet (the vertex of the parabola) the ball could be considered to be at t(0) and affected by gravity, but the ball still has horizontal motion as well, which I dont know if that can be determined...

anonymous · Answer

If i know the vertex is at (330,90) and the ball lands at (660,0) , then I know I guess we do know some things. The ball has to travel 330 feet horizontally in the time it takes to fall 90 feet.

anonymous · Answer

but using those gives the slope of a straight line between the vertex and the final location, not the nice arch of the parabola. I need some help here, I guess theres got to be a way to take those 2 bits of information and combine it with the parabola?

amistre64 · Answer

id say you can use time and gravity as parameters

amistre64 · Answer

the path can be defined by derivatives, which relate to the speed of the object at a given position

amistre64 · Answer

if you know speed, you can most likely define it in terms of time

amistre64 · Answer

or another thought ...

if you know height, then you know how far it has to drop under the effect of gravity.  which is half the time it takes to get from start to end of the arced path

amistre64 · Answer

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