
Physics Physics Forum 
 LinkBack  Thread Tools  Display Modes 
July 10th, 2019, 07:11 AM  #1 
Senior Member Joined: Aug 2014 From: India Posts: 405 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: 2,226 Thanks: 908 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: 405 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: 2,226 Thanks: 908 Math Focus: Wibbly wobbly timeywimey stuff.  Quote:
Dan  
July 10th, 2019, 09:29 PM  #5 
Senior Member Joined: Aug 2014 From: India Posts: 405 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: 2,226 Thanks: 908 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  

Tags 
formula, height, max, proper, trajectory, ymax 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Projectile Trajectory  prashantak  Physics  4  March 30th, 2019 03:35 PM 
Proper Divisors , Proper Multiples , Deficient , Abundant and Perfect Numbers  agentredlum  Number Theory  0  May 4th, 2017 10:35 AM 
max length of trajectory  triplekite  Calculus  2  October 19th, 2012 11:58 PM 
Sequence Trajectory  ZardoZ  Applied Math  17  November 17th, 2011 02:01 PM 
Height equilateral triangle  formula  e81  Algebra  4  May 18th, 2011 08:41 PM 