Kinematics equations with collision fo 2 balls

[mjolnir80]

Homework Statement

a ball is shot straight up from the ground with speed Vo. simultaneously, a second rubber ball at height h directly above the first ball is dropped from rest
at what height above the ground do the balls collide?asnwer should be a symbolic expression in terms of Vo and g.

Homework Equations

kinematics equations

The Attempt at a Solution

we can use (delta)x = Vot + 1/2 a t² and since we know that the final positions are equal we can write this equation for the 2 balls and make them equal to each other
but the equation of the second ball would have a x(initial) for the ball in the equation (assuming the base line is the ground)...

can someone help me out please. Thanks in advanced

 

[LowlyPion]

Homework Statement

a ball is shot straight up from the ground with speed Vo. simultaneously, a second rubber ball at height h directly above the first ball is dropped from rest
at what height above the ground do the balls collide?asnwer should be a symbolic expression in terms of Vo and g.

Homework Equations

kinematics equations

The Attempt at a Solution

we can use (delta)x = Vot + 1/2 a t² and since we know that the final positions are equal we can write this equation for the 2 balls and make them equal to each other
but the equation of the second ball would have a x(initial) for the ball in the equation (assuming the base line is the ground)...

can someone help me out please. Thanks in advanced

You mostly have it.
Construct the upward equation first:
X=Vo*t - 1/2*g*t²

Then construct the equation from rest:
X= h - 1/2*g*t²

If you solve for t then you just substitute into one of the x equations for the height.

 

[baba89]

.

To solve this problem, we can use the kinematics equations for both balls and set their final positions equal to each other. The kinematics equation for the first ball, which is shot straight up from the ground, is x = Vot - 1/2 gt^2. The kinematics equation for the second ball, which is dropped from rest at height h, is x = h + 1/2 gt^2. Setting these two equations equal to each other, we get Vot - 1/2 gt^2 = h + 1/2 gt^2. We can then solve for t, the time it takes for the balls to collide, by rearranging the equation to t = sqrt(2h/g). Finally, we can plug this value of t into either of the original equations to find the height at which the balls collide, which would be h + 1/2 gt^2. Therefore, the height at which the balls collide can be expressed as h + 1/2 (Vo^2/g).