A bomb is dropped from D from an aeroplane moving horizontally with a speed v. At the same instance another bomb is vertically projected with a speed u from the point B. what should be u so that the two bombs collide at E while bomb from B is going up.
 

 

 

 

 
 .............................(1)
$y_1=\frac{1}{2}g{t}_1^2=\frac{1}{2}g{\left(\frac{R}{2v}\right)}^2=\frac{g{R}^2}{8v^2}$  ....................(2)
For bomb from B
$y_2=u{t}_1-\frac{1}{2}g{t}_1^2=\frac{uR}{2v}-\frac{g{R}^2}{8v^2}$ ............................(3)
 
 
(2), (3) and (5)

 $\Rightarrow \frac{g{R}^2}{8v^2}+u\left(\frac{R}{2v}\right)-\frac{g{R}^2}{8v^2}=H$ 
$\therefore \frac{\mathrm{uR}}{2\mathrm{v}}=\mathrm{H}$  .............................(6)
(4) and (6) $\Rightarrow u=\frac{2vH}{R}=\frac{2v}{R}\cdot \frac{R^{2}g}{2v^2}$ 
$\therefore \text{u}=\frac{\text{gR}}{\text{v}}$