Acceleration due to gravity (challenging)

[kingwinner]

This question is very challenging for me! I attempted this question for almost an hour, but still can't complete it! I really need somebody to help me out!

 

1) A flowerpot is dropped from the balcony of an apartment, 28.5m above the ground. At a time of 1.00s after the pot is dropped, a ball is thrown vertically downward from the balcony one storey below, 26.0m above the ground. The initial velocity of the ball is 12.0m/s[down]. Does the ball pass the flowerpot before striking the ground? If so, how far above the ground are the two objects when the ball passes te flowerpot?

 

First of all, I calculated the travelling time of the flowerpot is 2.41s, and the travelling time of the ball is 1.38s.

 

Since the travelling time of the flowerpot minus travelling time of the ball =1.03s > 1.00s, the ball does pass the flowerpot before striking the ground. [by the way, is this true? Or is it the other way around? (i.e. the ball does not pass the flower pot?)]

 

And then I tried to introduce an unknown x = the height of the 2 objects above the ground when the ball passes the flowerpot, and got into a complete mess. I got into something that I can't solve for x (in my high school level)...

Is there an easy and fast way to find out "how far above the ground are the two objects when the ball passes te flowerpot"?

 

This question really get me frustrated...

[CraigD]

You should know the general equation for a body under uniform acceleration, in a form convenient for this problem (which may be a little different than you usually see it in):

Distance = Distanceinitial + Velocityinitial(Time – Timeinitial) + (Acceleration/2)(Time – Timeinitial)^2

 

See if you can fill in the given values to write this equation for the flower pot, then write it again for the ball (be careful to get the +/- signs right), set them equal, and solve for Time. Take either of the equations and plug in Time to get Distance. (best to plug it into both equations, to be sure you get the same distance – if not, you made a mistake in your algebra!)

 

None of the algebra is above high school level. The answer you’ll get depends a lot on what you use for Acceleration (eg: 10 m/s/s, 9.8 m/s/s, or something more precise), but works using any of these.

 

Post you answers and work when you’re done, or what you can if you get stuck.

 

PS: everybody keep their answers to themselves until the thread starter (kingwinner) has had a chance to answer.

[kingwinner]

You should know the general equation for a body under uniform acceleration, in a form convenient for this problem (which may be a little different than you usually see it in):

Distance = Distanceinitial + Velocityinitial(Time – Timeinitial) + (Acceleration/2)(Time – Timeinitial)^2

 

See if you can fill in the given values to write this equation for the flower pot, then write it again for the ball (be careful to get the +/- signs right), set them equal, and solve for Time. Take either of the equations and plug in Time to get Distance. (best to plug it into both equations, to be sure you get the same distance – if not, you made a mistake in your algebra!)

 

None of the algebra is above high school level. The answer you’ll get depends a lot on what you use for Acceleration (eg: 10 m/s/s, 9.8 m/s/s, or something more precise), but works using any of these.

 

Post you answers and work when you’re done, or what you can if you get stuck.

 

PS: everybody keep their answers to themselves until the thread starter (kingwinner) has had a chance to answer.

 

I think the first problem is whether the ball will pass the flowerpot! I got the travelling time of the flowerpot is 2.41s, and the travelling time of the ball is 1.38s, does this mean that the ball will pass the flowerpot? I am not too sure...

 

If the answer to the above question is yes, this brings me to the second question. I let the displacemnt of the flowerpot be -28.5+x and displacemnt of the ball be -26.0+x. And then find the time for both in terms of x and set up t(flowerpot)=t(ball)+1.0, but end up with something that have square roots and squares that can't be solved.......and also this method is time-consuming.....I am wondering if there are easier ways to do this question.

[CraigD]

I think the first problem is whether the ball will pass the flowerpot! I got the travelling time of the flowerpot is 2.41s, and the travelling time of the ball is 1.38s, does this mean that the ball will pass the flowerpot?

Yes, it does, but it’s not necessary to solve 2 separate problems to answer both questions (“will they pass?”, “where will they pass?”). Solving one equation for Time, determining Distance, will answer both. If Distance turns out to be negative (that is, underground), then they do not pass.

… but end up with something that have square roots and squares that can't be solved.......and also this method is time-consuming.....I am wondering if there are easier ways to do this question.

Try setting the 2 equations for Distance equal to one another and solving for Time. After collecting common terms, no squared terms will remain.

 

Using algebra to solve mechanics problems like this is an important technique. Once you’re comfortable with the techniques, I’d expect this problem to require 5 minutes or less to solve.