question_answer

At the height 80 m, an aeroplane is moved with 150 m/s. A bomb is dropped from it, so                 as to hit a target. At what distance from the                 target should the bomb be dropped? \[(g=10\,m/{{s}^{2}})\]

A)  605.3 m                              

B)         600 m

C)         80 m                                    

D)         230 m

Correct Answer: A

Solution :

Time taken by the bomb to reach the ground is given by \[{{h}_{OA}}=\frac{1}{2}gt_{OB}^{2}\] we have  \[{{t}_{OB}}=\sqrt{\frac{2{{h}_{OA}}}{g}}\] Given,   \[{{h}_{OA}}=80\,m,\,g=10\,m/{{s}^{2}}\] \[\therefore \]  \[{{t}_{OB}}=\sqrt{\frac{2\times 80}{10}}=4s\] Horizontal velocity of bomb \[v=150\,m/s\] Horizontal distance covered by the bomb \[AB=v{{t}_{OB}}\] \[=150\times 4\] \[=600\,m\] Hence, the bomb should be dropped 600 m before the target.