Motion of two balls which collide

[Faka]

A ball is thrown straight up from the ground with speed v₀. At the same instant, a second ball is dropped from rest from a height H, directly above the point where the first ball was thrown upward. There is no air resistance. How to I find the time at which the two balls collide. A how do I find the value of H in terms of v₀ and g so that at the instant when the balls colide, the first ball is at the heighest point of its motion.

Anybody who can help?

 

[tiny-tim]

Hi Faka!

Use standard https://www.physicsforums.com/library.php?do=view_item&itemid=204" equations,

with different values for s_i (the initial distance) …

what do you get? ​

 

[Faka]

Is it this equation I need to use s = u*t + 1/2*a*t^2 ?

 

[tiny-tim]

Yes.

 

[Faka]

Ball 1 (Going upward with a v0):

s1 = vo*t-0,5*g*t^2

Ball 2 (Dropped from a height H)

s2 = h-0,5*g*t

And then I need to find the time t:
s1 = s2

I get something crazy !

Is my method good?

 

[tiny-tim]

Hi Faka!

(try using the X² and X₂ icons just above the Reply box )

Ball 2 (Dropped from a height H)

s2 = h-0,5*g*t

you mean s₂ = h - 0,5*g*t²

otherwise, that's ok ​

 

[Faka]

Yes, its t^2 .
I think that I have made a mistake. Shouldn't it be:
Ball 1

s1 = Vo*t+0,5*g*t^2

Ball 2

s2 = h+0,5*g*t

Then
s1 = s2

I mean "+" instead of "-".

 

[Faka]

s2 = h+0,5*g*t^2

 

[tiny-tim]

it doesn't matter whether you use +g and g = -9.81, or -g and g = -9.81

show us your full calculations ​

 

[Faka]

Ball 1 (Upward)
x1 = 0 + v0*t + 1/2*(g)*t^2
= vo*t + g*t^2

Ball 2 (Dropped)
x2 = h + 0*t + 1/2*(-g)*t^2
= h - 1/2*g*t^2x1 = x2

vo*t + g*t^2 = h - 1/2*g*t^2And then I solve for t, I get something that I can't write here. Its something divided by 2*g

 

[tiny-tim]

Ball 1 (Upward)
x1 = 0 + v0*t + 1/2*(g)*t^2
= vo*t + g*t^2

Ball 2 (Dropped)
x2 = h + 0*t + 1/2*(-g)*t^2
= h - 1/2*g*t^2

No, you can't have g in one equation and -g in the other.