MHB Momentum of Falling Ball X & Ball Y: A Physics Puzzle

[Shah 72]

Ball X has mass 0.03kg. It falls vertically from rest from a window that is 30 m above the ground. Ball Y has mass 0.01kg. At the same time that Ball X starts to fall, Ball Y is projected vertically upwards from ground level directly towards Ball X. The initial speed of Ball Y is 20 m/s vertically upwards.

a) Find the downward momentum of each Ball just before they meet.

The Ball coalesce and the combined object falls to the ground.
b) show that the combined object reaches the ground 2.68 s after Ball X started to fall.
Pls help as I don't know how to solve.

 

[skeeter]

let $d$ be the distance above ground the two masses collide ...

$d = 20t - 5t^2$
$-(30-d) = -5t^2$

solve for $t$, the time of collision, and $d$

falling mass, $v_{f1} = 0 - 10t$
rising mass, $v_{f2} = 20 - 10t$

conservation of momentum ...

$Mv_{f1} + mv_{f2} = (M+m)V$, where $V$ is the velocity of the combined masses after the collision

you should have the position of collision and $V$ the initial velocity after the collision ... calculate the time necessary to hit the ground and add to the time of collision

 

[Shah 72]

let $d$ be the distance above ground the two masses collide ...

$d = 20t - 5t^2$
$-(30-d) = -5t^2$

solve for $t$, the time of collision, and $d$

falling mass, $v_{f1} = 0 - 10t$
rising mass, $v_{f2} = 20 - 10t$

conservation of momentum ...

$Mv_{f1} + mv_{f2} = (M+m)V$, where $V$ is the velocity of the combined masses after the collision

you should have the position of collision and $V$ the initial velocity after the collision ... calculate the time necessary to hit the ground and add to the time of collision

Thank you very much!