September 30th, 2017, 07:06 PM  #1 
Member Joined: Apr 2017 From: New York Posts: 52 Thanks: 4  velocity
If a ball is thrown vertically upward with a velocity of 144 ft/s, then its height after t seconds is s = 144t − 16t². a) What is the velocity of the ball when it is 320 ft above the ground on its way up? (Consider up to be the positive direction.) b) What is the velocity of the ball when it is 320 ft above the ground on its way down? Can you teach me how questions of this kind can be solved? Thanks. Last edited by skipjack; October 1st, 2017 at 02:43 PM. 
September 30th, 2017, 10:50 PM  #2 
Senior Member Joined: Sep 2015 From: USA Posts: 1,752 Thanks: 894 
$s(t) = 144t 16t^2$ a) $v(t) = \dfrac{ds}{dt} = 14432t$ now we need to determine at what time(s) the ball is 320 ft above the ground. $320 = 144t  16t^2$ $16t^2 144t + 320 = 0$ $t^2  9t + 20 = 0$ $(t5)(t4) = 0$ $t = 4s,~5s$ It should be clear that $t=4s$ corresponds with it being on its way up. so $v(4) = 14432(4) = 144  128 = 16ft/s$ b) Conveniently, we've already solved for $t$ corresponding to $s=320$ and it being on its way down. We did this in (a) and saw it to be $t=5s$ $v(5) = 144  32(5) = 144160 = 16 ft/s$ Last edited by skipjack; October 1st, 2017 at 02:53 PM. 
October 1st, 2017, 08:32 AM  #3 
Member Joined: Apr 2017 From: New York Posts: 52 Thanks: 4 
Thank you very much Romsek, that helped a lot. what I was doing was solving for t find t=4, 5 but I was plugging in into original equation (144t16t^2) instead of the derivative of the function. thanks thanks thanks 
October 1st, 2017, 10:32 AM  #4 
Member Joined: Apr 2017 From: New York Posts: 52 Thanks: 4 
this is great thanks. how about finding the maximum height the particle can reach? 
October 1st, 2017, 10:44 AM  #5 
Senior Member Joined: Sep 2015 From: USA Posts: 1,752 Thanks: 894  
October 1st, 2017, 12:08 PM  #6 
Member Joined: Apr 2017 From: New York Posts: 52 Thanks: 4 
velocity is zero at the maximum height. I equalize the f'(x) to zero and solve for the x and I see that t=4.5s which is the maximum height occurs at 4.5s so I plug it in my f(x) to see that the height is? is that so? 
October 1st, 2017, 01:05 PM  #7 
Senior Member Joined: Sep 2015 From: USA Posts: 1,752 Thanks: 894  

Tags 
velocity 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Initial Velocity, Final Velocity  IzzyD  Physics  3  June 3rd, 2017 01:29 PM 
Obtaining angular velocity given linear velocity and center of rotation 3D  quarkz  Calculus  0  April 18th, 2014 06:34 AM 
Velocity  arron1990  Calculus  7  May 31st, 2012 05:23 AM 
Velocity?  Kimmysmiles0  Algebra  1  April 27th, 2012 10:14 PM 
Velocity  instereo911  Calculus  5  February 24th, 2008 01:41 PM 