Ah! Please help! I'm about to lose power due to a very bad snow storm and this is the very last question I have from my online homework, and I just want to get this done before I am in the dark!
A ball is thrown across a playing field from a height of h = 3 ft above the ground at an angle of 45° to the horizontal at the speed of 20 ft/s. It can be deduced from physical principles that the path of the ball is modeled by the function
y= − (32 / (20)^2)x^2 + x + 3
(a) Find the maximum height attained by the ball. (Round your answer to three decimal places.)

Question

Ah! Please help! I'm about to lose power due to a very bad snow storm and this is the very last question I have from my online homework, and I just want to get this done before I am in the dark!
A ball is thrown across a playing field from a height of h = 3 ft above the ground at an angle of 45° to the horizontal at the speed of 20 ft/s. It can be deduced from physical principles that the path of the ball is modeled by the function
y= − (32 / (20)^2)x^2 + x + 3
(a) Find the maximum height attained by the ball. (Round your answer to three decimal places.)

anonymous · Answer

(b) Find the horizontal distance the ball has traveled when it hits the ground. (Round your answer to one decimal place.)

surry99 · Answer

so this a projectile motion question ...agreed?

anonymous · Answer

Yes.

surry99 · Answer

ok at it maximum height, what is the y component of the velocity of the ball?

anonymous · Answer

20 ft/s?

surry99 · Answer

No, at the top the vertical component of the velocity must be equal to zero

surry99 · Answer

you still there?

anonymous · Answer

Yes.

surry99 · Answer

do you agree about the y component at the top?

anonymous · Answer

yes

surry99 · Answer

great now the equation of motion describes an upside down parabola agreed?

anonymous · Answer

Yes.

surry99 · Answer

ok, what is the slope of the parabola when the ball is at the top?

surry99 · Answer

Draw a sketch if you need to...

surry99 · Answer

still there

anonymous · Answer

Yes, sorry. I'm trying to figure it out but I seriously do not know.

surry99 · Answer

That is ok...I will help you.
The slope of the parabola woould be zero at the top.  What does that mean
in terms of dy/dx?

surry99 · Answer

dy/dx would be equal to zero.
Since you are given y = f(x) you could take the derivative and set it equal to zero to find the corresponding value of x....agreed?

anonymous · Answer

Yes.

surry99 · Answer

ok go ahead and lets see what  you get....

anonymous · Answer

I got 9.125 for the max height

surry99 · Answer

so what value did you get for x and how did you get y...just want to make sure

anonymous · Answer

Used the formula k = c - (b^2/4a) *my professor said that is used to find the max height* but webassign wont take that answer. I mean, it's already rounded to three decimal places.

surry99 · Answer

hang on

surry99 · Answer

I have y = -(32/400)x^2 + x + 3 ...correct?

anonymous · Answer

yes.

anonymous · Answer

I got it now! My professor just sent out a mass email saying he gave us the wrong equation to find the max height and to find the distance. Thank you for your help though.

surry99 · Answer

so dy/dx = -.16x + 1
so 0 = -.16x +1
x=1/.16 = 6.25

then for the height y
y = -.08(6.25^2) + 6.25 + 3  
y = 6.125

surry99 · Answer

you are ok then or do you want me to help you finish

anonymous · Answer

Nope, I got it. Thank you though. I'll give you a medal for helping me with this roller coaster of a question.

surry99 · Answer

ok let me know if you need any help in the future.
Take care and stay warm in the storm.

anonymous · Answer

Alright and will do!