# Question on the free-fall of 2 bodies

1. Oct 29, 2016

### Mr.maniac

1. The probleas
statement, all variables and given/known data

Two stones are projected from the top of a tower 100m high each with velocity of 10m/s. One is projected upward while the other is projected downward. Find the ratio of velocity's by with which they strike the ground.

2. Relevant equations
S= ut +1/2(a)(t)^2
(v)^2-(u)^2=2as
v=u+at

3. The attempt at a solution
Let the stone projected upward be , body A
And the body projected downward be body B

For body A
(v)^2-(u)^2=2as
(v)^2-(100)=2(10)(100)
v=√(1900)
For body B before reaching max. height
(v)^2-(u)^2=2as
-(100)=(2)(10)(s)
5=s
For body B after reaching the max. height
(v)^2-(u)^2=2as
(v)^2=(2)(10)(105)
v=√(2100)

And I reached a dead end because
(10)(√21)/(10)(√19)

Ain't in the options

2. Oct 29, 2016

### PeroK

Maybe you could do this without using any equations?

3. Oct 29, 2016

### Mr.maniac

OK lemme see

4. Oct 29, 2016

### Mr.maniac

But the distance travelled by both the bodies is different

5. Oct 29, 2016

### PeroK

Try describing the motion of the ball that gets thrown up. Do you notice anything?

6. Oct 29, 2016

### Mr.maniac

OK wait a sec
Is it that the second body gains the same velocity as the first on whenn it is100m high

7. Oct 29, 2016

### PeroK

You mean if you throw a ball up at 10m/s, you know what speed it has when it comes back down to its starting point?

8. Oct 29, 2016

### Mr.maniac

v=u+at (before reaching its highest point)
0=10+10t
1=t
Then it would take 1s to come back to its starting point and
v=u+at( after reaching the highest point)
v=10m/s
So basically both bodies start from the same point with the same vel. So the velocity before reaching the ground would be the same hence the answer is 1:1

9. Oct 29, 2016

### Mr.maniac

Thanks for the help,

10. Oct 29, 2016

### PeroK

Yes, exactly. But, you may wish to go back to your equations and figure out how you got the wrong answer!

Hint: $s$ in the suvat equations is "displacement", not "total distance travelled".