If a ball is thrown directly upward with a velocity of 52 feet per second, its height (in feet) after seconds is given by y=52t-16t^2 . What is the maximum height attained by the ball

Question

If a ball is thrown directly upward with a velocity of 52 feet per second, its height (in feet) after  seconds is given by y=52t-16t^2 . What is the maximum height attained by the ball

anonymous · Answer

@physics aagain. eitherway what is the vertex of the parabola?

abb0t · Answer

You want to take the first derivative of the function and set it equal to zero.
The value you get when you solve for "t" after taking the derivative is the number you are plugging in for "t"
in your original 52t-16t^2 equation

anonymous · Answer

depending if you want to use calc or not.

anonymous · Answer

its precalc

abb0t · Answer

Well, this is a typical Calc question, so I just assumed, but i guess assuming isn't helping me today :'''''(

abb0t · Answer

Are you familiar with the definition of the derivative? Such as limits?

anonymous · Answer

just starting them so not too familiar but i understand some

abb0t · Answer

I think this is the definition, you might want to re-check your book. but it's sort of like using (f o g).
$$\frac{ f(a)-f(t) }{ t-a }$$

anonymous · Answer

ok yes we just covered that

anonymous · Answer

Since you're in pre-calc, the method of solving the maximum height is going to beby determining the vertex, just as you were asking and suggesting.  Re-writing:

y = -16t^2 + 52t            y = -16(t^2 - (13/4)t)

y = -16(t^2 - (13/4)t +169/64) + 169/4

y = -16(t - 13/8)^2 + 169/4

So, at t = 13/8, you have a maximum height of 169/4

That makes the vertex (13/8, 169/4).

You could also arrive at this answer by using differential calculus, but this method was detailed since you asked for the vertex and you mentioned that you are in pre-calc, not calc.

anonymous · Answer

All good now, @samancha85 ?  If you have any question, just ask and we can go over any part of this in greater detail

anonymous · Answer

Good luck to you in all of your studies and thx for the recognition!  @samancha85

anonymous · Answer

ok where did the 13/4 com from

anonymous · Answer

The 13/4 came from:

-13/4 times -16 = 52

We had to get the "t" term inside of the parentheses so that we could complete the square.

anonymous · Answer

That would eplain the firstline, right side.  We have 169/64 within the parentheses to get the actual square.  Then we added 169/4 because we essentially subtracted 169/4 with the -16 times 169/64 within the parentheses.  Then we put the exponent on the outside in the usual method of doing these.

anonymous · Answer

The 169/64 came from taking half of 13/4 and squaring that.  That's the key to the problem, the "completing the square" part.

anonymous · Answer

ok great thank u that makes sense now! :)