- #1

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I believe this is a related rates problem.

I attempted part 2 but I'm not sure about the equation for the maximum height. is it the derivative ?

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- Thread starter asdfsystema
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- #1

- 87

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I believe this is a related rates problem.

I attempted part 2 but I'm not sure about the equation for the maximum height. is it the derivative ?

- #2

Mark44

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The function you're given describes the height of the ball relative to time. What is the shape of this graph? The high point of the graph tells you the height of the ball at its highest position, and the time when it gets there.

For the second part, your derivative is correct, but if you evaluate the derivative at t = 0, what you're getting is the velocity at t = 0. IOW, the velocity when the ball is thrown.

Use your given function to find when s(t) = 0. Whatever time you get is the time when the ball hits the ground. Use that value in your velocity function to find the ball's velocity when it hits.

- #3

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- #4

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it is a parabola with a max , so the maximum height will be at the max point in the graph.

s(t) = 48t+64t-16t^2

take derviative . s'(t) = 64 -32t

set to zero t= 2 . plug t back in original?

48(2)+64(2)-16(2)^2 = 160

Part B.

i did what you suggested.

s(t) = 48+64t-16t^2 = 0

I get -(t+1) (t+4) sooo t= -1 and t=-4 ??

i know what to do next but im getting two "t" values right now ..

- #5

Mark44

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To clarify what you wrote,part A.

it is a parabola with a max , so the maximum height will be at the max point in the graph.

s(t) = 48t+64t-16t^2

take derviative . s'(t) = 64 -32t

set to zero t= 2 . plug t back in original?

48(2)+64(2)-16(2)^2 = 160

s'(t) = 0 ==> t = 2

s(2) = 160

Your calculations are correct, but what are the units here? Many instructors require that you state your answer in words.

You started with an equation: 48 + 64t - 16t^2 = 0.Part B.

i did what you suggested.

s(t) = 48+64t-16t^2 = 0

I get -(t+1) (t+4) sooo t= -1 and t=-4 ??

Each step should be an equation.

If I multiply the factors you show, I get -t^2 - 5t -4. Is that related to what you started with?

i know what to do next but im getting two "t" values right now ..

- #6

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I meant (-t-1)(t+3)

which will give me -t^2-4t-3 and is the same as -16t^2+64t+48 after dividing the whole thing by 16.

What is my next step ?

- #7

Mark44

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Also, each step should be an equation.

- #8

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ok i factored it again

x= 4.6457

x= -0.6457

What do I do next ... ?

x= 4.6457

x= -0.6457

What do I do next ... ?

- #9

Mark44

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What do they represent in terms of this problem? (You have them as values of x, but the original equation doesn't involve x.)

As for "what do I do next?" look at the original problem and try to understand what it is that you are doing. What you have done is find values for which s(t) = 0. Do you understand why you needed to do that, and what you have to do next? If you don't, take a look at message #2.

- #10

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s(t) = 48+64t-16t^2

v(t)= 64-32t

v(4.6457)= 64-32(4.6457)

v(t) = -84.6624

is that correct ?

v(t)= 64-32t

v(4.6457)= 64-32(4.6457)

v(t) = -84.6624

is that correct ?

- #11

Mark44

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The numbers look about right. What are the units?

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