Two spherical balls having equal masses with radius of 5 cm each are thrown upwards along the same vertical direction at intervals of 3s with the same initial velocity of 35 m/s, then these balls collide at a height of ____ m.   

(Take, $g=10m/s^2$) 

Given, $m_1=m_2=m$

$r_1=r_2=r–5cm=5\times {10}^{-2}m$

$u_1=u_2=55m/s;t_1=0;t_2=3s$

 
When both ball will collide, 
${\left(S_1\right)}_{vertical}={\left(S_2\right)}_{vertical}\dots \dots .\left(i\right)$

Let after time both ball will collide.

$\begin{array}{l}{\left(S_1\right)}_{vertical}=ut-\frac{1}{2}g{t}^2\\ {\left(S_1\right)}_{vertical}=u_2(t-3)-\frac{1}{2}g{(t-3)}^2\end{array}$

From Eq. (i) we have

$\Rightarrow u_{1}t-\frac{1}{2}g{t}^2=u_2(t-3)-\frac{1}{2}g{(t-3)}^2$

$\Rightarrow 35t-\frac{1}{2}10X{t}^2=35(t-3)-\frac{1}{2}X10{(t-3)}^2$

$\Rightarrow 35t-35(t-3)=5t^2-5{(t-3)}^2$

$\Rightarrow 35(t-t+3)=5[t^2-{(t-3)}^2]$

$\Rightarrow 35X3=5(t+t-3)(t-t+3)$

$\Rightarrow \frac{105}{5}=(2t-3)\left(3\right)\Rightarrow \frac{21}{3}=2t-3\Rightarrow 7=2t-3$

$2t=10\Rightarrow t=5s$

$Sotheheightatwhichballwillcollideis$

${\left(S_1\right)}_{vertical}=u_{1}t-\frac{1}{2}g{t}^2=34X5-\frac{1}{2}X10X{\left(5\right)}^2=175-125=50m$