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July 10th, 2019, 07:11 AM  #1 
Senior Member Joined: Aug 2014 From: India Posts: 470 Thanks: 1  What is the proper formula for Max height & Ymax for this trajectory?
Trajectory: Time it takes from A to travel to B; $\displaystyle T = \large\frac{Vsinθ}{g}$ Time it takes for for B to travel to C; $\displaystyle T = \large\sqrt\frac{2y_{max}}{g}$ Then what is the formula for Max height & $\displaystyle Y_{max}$? 
July 10th, 2019, 12:08 PM  #2  
Math Team Joined: May 2013 From: The Astral plane Posts: 2,267 Thanks: 934 Math Focus: Wibbly wobbly timeywimey stuff.  Quote:
You really shouldn't use T to denote two different times. And, personally, I'd change the label V to $\displaystyle V_0$ or something. Dan Last edited by topsquark; July 10th, 2019 at 12:13 PM.  
July 10th, 2019, 07:40 PM  #3 
Senior Member Joined: Aug 2014 From: India Posts: 470 Thanks: 1  What is $\displaystyle y$, $\displaystyle y_{0}$,$\displaystyle v_{0y}$,$\displaystyle V$ & $\displaystyle H$?

July 10th, 2019, 08:30 PM  #4  
Math Team Joined: May 2013 From: The Astral plane Posts: 2,267 Thanks: 934 Math Focus: Wibbly wobbly timeywimey stuff.  Quote:
Dan  
July 10th, 2019, 09:29 PM  #5 
Senior Member Joined: Aug 2014 From: India Posts: 470 Thanks: 1 
Still can't figure out formulae of $\displaystyle Y_{max}$. So what is the final formulae for $\displaystyle Y_{max}$?

July 11th, 2019, 09:23 AM  #6  
Math Team Joined: May 2013 From: The Astral plane Posts: 2,267 Thanks: 934 Math Focus: Wibbly wobbly timeywimey stuff.  Quote:
$\displaystyle s  s_0 = vt + \dfrac{1}{2}at^2$ $\displaystyle v = v_0 + at$ $\displaystyle s  s_0 = \dfrac{1}{2} ( v_0 + v) t$ $\displaystyle v^2 = v_0 ^2 + 2a(s  s_0)$ Where s is the displacement in a given direction. (I have changed to s instead of y because most texts start out that way.) These are the equations of motion of an object with a constant acceleration. In this case a = g. In this case let's look at the motion in the y direction. I'm going to set an origin at the bottom of the cliff directly below where the object was launched, and +y is upward. So we know at what height the object was thrown (or whatever): $\displaystyle s_0 = H$ and it was launched at a speed V at an angle $\displaystyle \theta $ above the horizontal: so $\displaystyle v_0 = V ~ sin( \theta )$. You are looking for the max height, $\displaystyle s_{max}$, which is where the vertical component of the velocity $\displaystyle v = 0$. So what equation(s) do we have where we know the values of a, $\displaystyle s_0$, $\displaystyle v_0$, and v and we are looking to find s? There's only one of them in the list. Dan  

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formula, height, max, proper, trajectory, ymax 
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