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Old May 16th 2009, 02:12 PM   #1
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Two balls one thrown one dropped from a building

A ball is thrown straight up from the edge of the roof of a building. A second ball is dropped from the roof a time of 1.19s later. You may ignore air resistance.


Part A)If the height of the building is 19.4m, what must the initial speed be of the first ball if both are to hit the ground at the same time?

Part B)
Consider the same situation, but now let the initial speed vo of the first ball be given and treat the height h of the building as an unknown. What must the height of the building be for both balls to reach the ground at the same time for vo=9m/s

Part C)If vo is greater than some value vmax, a value of h does not exist that allows both balls to hit the ground at the same time. Solve for vmax.

Part D)
If vo is less than some value vmin, a value of h does not exist that allows both balls to hit the ground at the same time. Solve for vmin.

I have an exam on monday and I can't find the solution or remember how to do it.

Any help?
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Old May 17th 2009, 10:22 PM   #2
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Use s = ut + 0.5 gt^2 for the 2nd ball with u the initial vel =0.
So, 19.4 = 0.5 x 9.8 x t^2 and t = 1.989 sec. The total time taken by the 1st ball is therefore 1.19+1.989 = 3.18 secs. We can split up this 3.18 secs as follows. The time taken by the ball to reach maximum height and return to the roof point say t1 and the time t2 taken to fall thru 1.94 metres with an initial vel of say u.
The time take to reach highest point is given by 0= u 98.t or t = u/g . Since there is no air resistance and the problem is symmetric , the time taken to reach back to the roof is also the same and the magnitude of the vel is also the same as u tough now pointing downwards.

So t1 = 2t = 2u/g. We have 1.94 = ut2 + 0.5 g (t2)^2. Now use t1+t2 = 3.18 secs also and solve. You should get an equation in terms of u.
I have used u instead of v0 .
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Old May 17th 2009, 10:33 PM   #3
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For part B, the problem is the same only the unknown quantity is different, so you should be able to solve.

For C and D, set up the equations using varaiables and examine them to see if you get a physically unacceptable result like t becoming -ve for the reqiured conditions.
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