Posted by steve on March 31, 19101 at 22:32:44:
In Reply to: Velocity posted by Taylor on September 12, 19100 at 16:40:49:
Hi there!
I think I may be able to help out here... first of all, the problem requires that you be familiar with a few forms of the free fall equations, (more specifically one-dimensional motion with constant acceleration). Let's begin.
They already give you that the stone takes .3s to travel 2.2m. So your first goal will be to find out what the velocity of the stone was just as it hit the top of the window. To do that, you use the following equation:
x=Vot+.5at^2
where 'x' is the distance traveled, 'Vo' is the original velocity (in this case the velocity of the stone when it hit the top of the window), 't' is the time interval, and 'a' is the acceleration due to gravity (since we're on Earth, and very near to sea level, that number is about 9.8m/s^2)
So,
x=2.2m
t=.3s
a=9.8m/s^2
2.2m=Vo(.3s)+.5(9.8m/s^2)(.3s)^2
2.2=.3Vo+4.9(.09)
2.2=.3V0+.441
2.2-.441=.3Vo
1.759=.3Vo
1.759/.3=Vo
5.863333m/s=Vo
So the velocity of the stone as it reached the top of the window was 5.8633333m/s. The next step is to find out how far above the window the stone was dropped from, in order to do that you need to use the following equation:
Vf^2=Vo^2+2ax
In this equation the Vo we found in the previous problem becomes Vf which is the final velocity here. And the Vo for this equation becomes 0 m/s. So you get the following
Vf=5.8633333m/s
Vo=0m/s
a=9.8m/s^2
5.863333^2=0^2+2(9.8)x
34.37867777=0+19.6x
34.37867777/19.6=x
1.754m=x
So the stone was dropped from a height of 1.754 meters above the top of the window. I know that seems like a lot of work, but after you get to know those equations more, and with the help of your calculator to do the math quickly, you'll breeze through problems like that:)
Hope I helped ya... Until we meet again, have a very pleasant day!
Steve
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