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Calculus-based physics-Please help solve this problem!

 
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pnwokolo



Joined: 11 Mar 2010
Posts: 11
Location: Toledo,OH

PostPosted: Sat Apr 24, 2010 5:40 am    Post subject: Calculus-based physics-Please help solve this problem! Reply with quote

Dear Site Admin,
Please help solve this physics problem for me. I have tried to solve but I can't get it right.
The question is:
You decide to drop a melon from rest from the first observation platform of the Eiffel Tower. The initial height
h from which the melon is released is 58.3 m above the head of your French friend Pierre, who is standing on the
ground right below you. At the same instant you release the melon, Pierre shoots an arrow straight up with an
initial velocity of 251.m/s.
(a) At what height above Pierre’s head do the melon and the arrow collide?
(b) What are the velocities of the melon and the arrow at the moment of collision?
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hepcj
Site Admin


Joined: 23 Jun 2007
Posts: 125

PostPosted: Sun Apr 25, 2010 10:27 pm    Post subject: Reply with quote

In this problem you need to work out the time it takes for the object which is dropped and the time it takes for the arrow and then equate them and solve for t. This will give the time at which they meet. You can then substitute the value of the t in either one of the equations to find the height at which they hit each other.

Hint. Use the equations of motion:
s(t) = s0 + u t + 0.5 g t^2

where s(t) is the positions as a function of time.
s0 is the initial position
u is the initial velocity
g is the gravitational acceleration

Taking the origin at Pierre's head. The equations for the position are
s(t) = 251 t + 0.5 g t^2 for the arrow
and
s(t)= 58.3 + 0.5 g t^2 for the melon

solving for t we find that the that t= 0.232271 sec.

this gives a height of 58.354 m (this is because the speed of the arrow is so fast that the melon hardly has any time to fall.)

For part b)

v(t) = u0 + g t
For the arrow v = 248.72 m/s
For the melon
v(t) = g t (since it starts at zero velocity)
-2.27858 m/s
since it is falling in the opposite direction.
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larry



Joined: 15 Mar 2010
Posts: 1
Location: Denver, Colorado

PostPosted: Mon Apr 26, 2010 1:35 am    Post subject: Reply with quote

How can the height they meet at be higher than the height the melon was dropped at?
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pnwokolo



Joined: 11 Mar 2010
Posts: 11
Location: Toledo,OH

PostPosted: Mon Apr 26, 2010 2:05 am    Post subject: calculus-based physics! Reply with quote

Dear Site Admin.
Thanks very much. I am very grateful for your help. There was a question below your answer asking why is the height at which they meet higher than the initial height at which the melon was released? Can you please explain to me if you wouldn't mind, I will highly appreciate that.
Once again, thank you very much for everything.
Patrick Nwokolo
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hepcj
Site Admin


Joined: 23 Jun 2007
Posts: 125

PostPosted: Mon Apr 26, 2010 8:56 am    Post subject: Reply with quote

My mistake. There is a sign wrong somewhere. The method is sound, however. I will take another look at my calculations.
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hepcj
Site Admin


Joined: 23 Jun 2007
Posts: 125

PostPosted: Mon Apr 26, 2010 10:08 pm    Post subject: Reply with quote

I have looked at my answer again. It is not a mistake with the signs I just copied it into the reply wrongly. The answer is 58.0354 m not 58.354 m.
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