# Relative velocities of balls on reaching the ground.

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1. Jun 3, 2015

### takando12

Here's a physics question that's been giving me trouble. At a height H ,a ball A is thrown upward with a velocity of 20m/s and another B one is thrown down with a velocity of 20m/s and a third ball C is just dropped. Note that it's the same height for all three.I need to find the relation between their velocities when they hit the ground.
attempt at solving:
A - The velocity on hitting the ground must be the same as the projected velocity. So I think it's 20 m/s
B - Since it starts with 20m/s it's definitely going to speed up, so it's reasonable to assume that it's final velocity will be greater than A's.
C-This is where i'm confused. Using the formula v=u+gt and u=0 . v=gt .So the final velocity of C is solely dependent on t. Taking the falling part of A's journey, u=0 and v= 20m/s( from first assumption) using v=u+gt. gt=20 . Is the time for the falling of A and C the same and so the answer is A=C<B ?How do i proceed? I'm stumped.

2. Jun 3, 2015

### theodoros.mihos

Are the sing of $u$ the same?

3. Jun 3, 2015

### Sagar Singh

i can easily answer this question, but i can not understand that what kind of relation you want? can you please post the original question statement?

4. Jun 3, 2015

### takando12

The last part of the question says " Find the relation between their velocities when they hit the ground"
there are options as well like A=B>C , A>B>C, A=C<B. Meaning of the course the velocity of A,B,C.

5. Jun 3, 2015

### A.T.

Try energy conservation.

6. Jun 3, 2015

### Sagar Singh

Brother this question not for solving it can easily be solved with just common sense , A is going upward with 20 m/s so after reaching H it will be 20m/s downward, so final velocity of A and B will be same, c is just dropped, and relative acceleration is 0, so difference between velocities V(a or b)- V(c)=20m/s

7. Jun 3, 2015

### takando12

how can the final velocity of B be 20m/s? it's starting with 20m/s from the top and it will speed up right? it's accelerating under gravity so it should increase from 20m/s ? please correct me if i am wrong.

8. Jun 3, 2015

9. Jun 3, 2015

### theodoros.mihos

Write the energy conservation condition for the three cases.

10. Jun 3, 2015

### Sagar Singh

i said difference between velocities, not actual velocities, we don't know time, we don't know height, so we cannot find actual velocity.

11. Jun 3, 2015

### takando12

"so final velocity of A and B will be same"
you said the final velocity of A and B will be the same. A's final velocity is 20m/s, but B starts with 20m/s and speeds up right? so how can their final velocities be the same?
or does the velocity of B just be constant throughout the entire downward journey?

12. Jun 3, 2015

### Sagar Singh

A will go upward, reach a certain height, calculating, h=u*u/2g= 20m
ar an height of 20+H it will stop and start falling, when it falls 20. its velocity will be =20m/s, so both A and B will fall rom 20m/s downward.

13. Jun 3, 2015

### Drakkith

Staff Emeritus
Takando12, this should have been posted in the introductory physics homework section, per the rules. If you still require help, please start a new thread there.

For the rest of you, please do not answer homework or homework-style questions that have been posted outside of the homework forums. Use the report function to bring them to the attention of the mentors.