I am [make that: WAS] having difficulties solving Problem 87 from Chapter 2 of Physics for Scientists and Engineers by Paul A. Tipler, 4th edition. The statement of the problem is as follows:(adsbygoogle = window.adsbygoogle || []).push({});

Ball A is dropped from the top of a building at the same instant that ball B is thrown vertically upward from the ground. When the balls collide, they are moving in opposite directions, and the speed of A is twice the speed of B. At what fraction of the height of the building does the collision occur?

My incomplete [<Ahem> Make that: COMPLETE] attempt at a solution goes as follows:

We denote the height of the building ash, the position of ball A asy, the initial position of ball A as_{A}y, and analogously for ball B._{A0}

The equation of motion for ball A is the following:

yTherefore,_{A}- y_{A0}= v_{A0}t - (0.5)gt^{2}

y_{A0}= h

v_{A0}= 0

g = 9.81 m/s^{2}

y_{A}= -(0.5)(9.81 m/s^{2})t^{2}+ h

=> y_{A}= -4.905t^{2}+ h

The equation of motion for ball B is the following:

yTherefore,_{B}- y_{B0}= v_{B0}t - (0.5)gt^{2}

y_{B0}= 0

g = 9.81 m/s^{2}

y_{B}= v_{B0}t - (0.5)(9.81 m/s^{2})t^{2}

=> y_{B}= v_{B0}t - 4.905t^{2}

The two balls collide wheny:_{A}= y_{B}

y_{A}= y_{B}=> -4.905t^{2}+ h = v_{B0}t - 4.905t^{2}

=> h = v_{B0}t

For ball A:

vTherefore,_{A}= v_{A0}- gt

v_{A0}= 0

v_{A}= - gt => v_{A}= -9.81t

For ball B:

vTherefore,_{B}= v_{B0}- gt

v_{B}= v_{B0}- gt => v_{B}= v_{B0}- 9.81t

We also know that wheny,_{A}= y_{B}v:_{A}= -2v_{B}

v_{A}= -2v_{B}=> -9.81t = -2[v_{B0}- 9.81t]

=> -9.81t = -2v_{B0}+ 19.62t

=> 2v_{B0}= 29.43t

=> v_{B0}= 14.715t

Sinceh = v, we have:_{B0}t

h = (14.715t)t = 14.715t^{2}

Unfortunately, I couldn't figure out what to do from this point until I spent the better part of the last hour typing this thread. :grumpy: Then, as I was typing the previous sentence, it hit me:

x_{A}= -4.905t^{2}+ h = -4.905t^{2}+ 14.715t^{2}

=> x_{A}= 9.81t^{2}

Therefore,x, which is the answer given in the back of the book._{A}/ h = 9.81t^{2}/ (14.715t^{2})

=> x_{A}/ h = 2/3

=> x_{A}= 2h/3

I've decided to post this thread anyway, partly because someone else might benefit from seeing it, and partly because I spent nearly an hour typing it.

This also reminds me of a post by Clausius2 in a previous thread I had posted:

I don't think this would have worked the last time, but it certainly worked here! :rofl: Clausius2 said:Maybe the time you have spent writing such [an elaborate] thread you could have re-written your solution of the problem, and surely you would find the error.

Oh brother ... Good night, everyone! :zzz:

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Another kinematics problem solved at the last second

**Physics Forums | Science Articles, Homework Help, Discussion**