My Math Forum find the average speed of the ball

 Calculus Calculus Math Forum

 September 19th, 2013, 03:50 PM #1 Newbie   Joined: Sep 2013 Posts: 1 Thanks: 0 find the average speed of the ball the height in ft of a baseball, t seconds after being thrown straight upward, is given by h(t)=36t - 16t^2 1) find the average speed of the ball for a) 0? t ?1 b) .5? t ? 1 c) .9 ? t ?1 the answer to a) is 20 ft/sec, which is what you get if you plug 1 into the equation. the answer to b) is 12 ft/sec, and c) is 5.6 ft/sec. how the heck did they get these answers?? I just don't get it. please explain how to do this step by step also it asks to estimate the speed of the ball after 1 second
 September 19th, 2013, 05:09 PM #2 Senior Member     Joined: Jul 2012 From: DFW Area Posts: 628 Thanks: 92 Math Focus: Electrical Engineering Applications Re: find the average speed of the ball Hi coolbeans33, and welcome to the forums. Differentiate h(t) to find v(t), the speed* of the ball. You will see that the equation is linear in t, so to find the average, you can simply add the values at the endpoints and divide by 2. You should get the answers that you stated. As far as the estimate is concerned, gravity reduces the speed of the ball by 32 ft/s each second. So after 1 second, subtract 32 ft/s from the initial speed to find the speed of the ball. But this is exactly how you would calculate it using the equation for v(t). I guess the problem says estimate since the 32 ft/s is not very precise. * The derivative of position is technically the ball's velocity rather than speed, meaning that it has direction, but in this case we can ignore direction and take the calculated value as the ball's speed.
 September 21st, 2013, 08:00 AM #3 Math Team   Joined: Sep 2007 Posts: 2,409 Thanks: 6 Re: find the average speed of the ball This looks to me like an "introduction to the derivative" type problem so differentiation might not be appropriate. (And, it works in this case, as jks said, only because the velocity function is linear.) In any case it is much simpler to use the basic definition of "average speed". To find the average speed, in ft/sec, find the distance it has moved and divide by the time required: The average speed between t= 0 and t= 1 is $\dfrac{h(1)- h(0)}{1- 0}$. The average speed between t= 0 and t= 0.5 is $\dfrac{h(0.5)- h(0)}{0.5- 0}$, etc.

 Tags average, ball, find, speed

,

,

### average speed of the ball between a and b

Click on a term to search for related topics.
 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post RealMadrid Physics 0 September 10th, 2012 07:53 AM xinglongdada Real Analysis 3 June 8th, 2012 12:13 AM haftakhan Algebra 1 August 11th, 2011 11:14 PM sivela Calculus 1 January 26th, 2010 09:10 PM EkajArmstro Algebra 2 March 12th, 2009 09:10 AM

 Contact - Home - Forums - Cryptocurrency Forum - Top