When will they collide?

Ball $b_{1}$ and the plank collide at $t = 1$ sec.

It is important to understand that the collision is elastic and the plank continues to move with $v = 5~ m/s$ after the collision.

The speed of the ball just before collision is $u = gt, u = 10~m/s$

The speed of the ball after collision $v_{f1}$ can be found out by equation of restitution. Since, collision is elastic, $e =1$

$v_{f1} - 5 = 1( 5 - (-10) )$

$v_{f1} = 20~ m/s$ upwards.

Now the problem is converted into a simple kinematics problem.

At $t = 1$ sec, just after the collision $b_{1}$ is at a height of $5~m$ and $b_{2}$ is at a height of $40 - \frac{1}{2}gt^{2} = 35 ~m$ .

Speeds of the balls are respectively, $v_{f1} =20~m/s$ and $v_{f2} =10~m/s$

Using equations of kinematics, $T$ can be easily found out.

$30 = v_{f1}(T -1) - \frac{1}{2}g(T-1)^{2} + v_{f2}(T-1) + \frac{1}{2}g(T-1)^{2}$

Thus,

$T = 2$ sec.