The problem contains graphics that I don't know how to show other than in an image format:
h t t p : / / b i t . l y / c D H P V M
h t t p : / / b i t . l y / 9 m b y C R
And I still haven't gotten an answer for my previous question here:
h t t p : / / b i t . l y / d g 6 o O F
I can't make the "previous" graphic open.
On this problem, label the horizontal distance H (dcosPHI) and the final height yf(dsinPHI)
horizontal:
VcosTheta*time=x=dcosPHI
vertical
yf=VsinTheta*time-1/2 g t^2
from the first equation
time=dcosPHI/VcosTheta
and putting this in the second equation
dsinPHI=VsinTheta*dcosPHI/VcosTheta-1/2 g (dcosPHI/VcosTheta)^2
multiplying both sides by (VcosTheta)^2
dsinPHI(VcosTheta)^2=V^2 sinThetacostheta d cosPHI=1/2 g dcosPHI
so take the derivative of d with respect to theta, set to zero, solve for theta in terms of V and PHI.
A bit of algebra is required, so get a large pad of paper.
What does d= ?
(Not sure what to take the derivative of)
d is the height up the hill, as drawn on your figure. As I recall, you are trying to maximize d, so d d/dTheta=0=..
To view the graphics in the links you provided, you can follow these steps:
1. Copy the first link: h t t p : / / b i t . l y / c D H P V M.
2. Open a new web browser tab or window.
3. Paste the link into the address bar of the browser.
4. Press Enter or Go.
5. This will take you to the Bitly website, which is a link shortening service. It automatically redirects you to the actual URL.
6. You should see the actual URL of the image, which might end in an image file extension like .jpg, .png, or .gif.
7. Right-click on the image and select "Open image in new tab" or a similar option.
8. The image should now open in a new tab in your web browser, allowing you to view it.
Repeat the same process for the second link: h t t p : / / b i t . l y / 9 m b y C R, to view the second image.