Standing On The Shoulders Of Giants - Average Velocity From 2 To 3 Seconds

Calculus Level 1

By dropping cannonballs off the top of the leaning tower of Pisa, Galileo demonstrated that the time taken for two balls of different masses to hit the ground is independent of its weight (if the amount of air resistance is similar). This experiment was repeated again in 2009, and you can watch Dan Falk's video of the event (skip to 2:00).

time t t 0 1 2 3 4
height h h 0 5 19 44 56

Assuming that the above table indicates the vertical height h h that the cannonballs dropped t t seconds after being released till it hits the ground and comes to rest. What is the average velocity from the second second to the third second?

Image credit: Wikipedia Theresa Knott
14 44 10 25

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Chung Gene Keun by Chung Gene Keun , 42, USA

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6 solutions

Discussions for this problem are now closed

Vivek Sedani
Apr 14, 2014

As we can see that at time t=3 sec the height was 44 and at t=2 sec the height was 19. So distance covered is 25. And Hence the average velocity is 25/(3-2) = 25. ...

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Aaditya Khare
Apr 19, 2014

Average velocity = ds/dt...so ds= 44-19=25 and dt = 3-2=1...ds/dt=25/1=25

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Aakash Amish
May 9, 2014

velocity in a distance time graph is the slope. Hence the slope here is (change in height)/(change in time) = (44-19)/(3-2) = 25

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Hannah DeMesa
Apr 30, 2014

Velocity is displacement over time, so just subtract the velocity of the object on second three from its previous velocity in second 2 divided by the time which is just a second. (44-19) = (25/1) = 25.

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Tran Duc
Apr 17, 2014

I think the table is wrong. The height should be the other way around, from 56 to 0.

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It is the vertical height that the cannonball has fallen, as opposed to the height at which the cannonball is at.

Chung Gene Keun - 7 years, 1 month ago
Mardokay Mosazghi
Apr 14, 2014

This is rather an easy problem if you know the basic formula D T \frac{D}{T} is equal to velocity.Then to find the average velocity just do 44-150}\ ({3-1} which is equal to 25 \boxed{25}

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