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## DLS 2 years ago At the same instant that a 0.50-kg ball is dropped from 25 m above Earth, a second ball, with a mass of 0.25 kg, is thrown straight upward from Earth’s surface with an initial speed of 15 m/s. They move along nearby lines and pass without colliding. At the end of 2.0 s the velocity of the center of mass of the two-ball system is:

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1. mayankdevnani

options??

2. DLS

A. 11 m/s, down B. 11 m/s, up C. 15 m/s, down D. 15 m/s, up E. 20 m/s, down

3. DLS

V(a)=20m/s V(b)=-5m/s

4. mayankdevnani

Since this is multiple choice, lets use 10 m/s^2 as the acceleration due to gravity.

5. DLS

so 0.50*20+0.25*(-5)/0.75

6. mayankdevnani

The trick is to look at the momentum of the system after 2 seconds. So for the heavy ball, after two seconds, it has a velocity of -20 m/s.

7. DLS

10+1.25/0.75 (wil we have a minus sign or are we considering just the mag?

8. mayankdevnani

Thus it has a momentum of -10 kg*m/s.

9. DLS

u took downwards negative?

10. mayankdevnani

yaa, i took downwards negative. The light ball will have a velocity of -5 m/s (15 m/s going up minus 20 m/s due to gravity gives 5 m/s downward). So it has a momentum of -1.25 kg*m/s.

11. mayankdevnani

In both cases, the negative sign indicates the momentum is downward, and the sum is -11.25 kg*m/s.

12. mayankdevnani

Find the velocity of the system by dividing by the total mass (0.75 kg)?? then solve it and you get your answer.

13. DLS

i took downwards positive and upwards negative,im getting something different

14. mayankdevnani

no, always took downwards negative and upwards positive

15. DLS

v=0+10*2 v=20m/s downwards and v=15-20 v=-5m/s upwards

16. mayankdevnani

no!!!!

17. mayankdevnani

Find the velocity of the system by dividing by the total mass (0.75 kg) and you get 15 m/s down. so your answer is option C) 15 m/s up.

18. DLS

wait u messed up!!

19. mayankdevnani

no,, 15 m/s down.

20. DLS

im taking downwards negative and upwards positive so for the 0.25 kg ball, v=15+20=35? we are taking upwards positive right

21. mayankdevnani

right

22. DLS

0.25*35=8.75

23. DLS

-20+8.75

24. DLS

oh :o

25. DLS

-11.25/0.75=-15m/s

26. DLS

i see! :D

27. mayankdevnani

okk

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