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: B

Solution :

Time taken by the bomb to reach the ground is given by \[{{h}_{{{O}_{A}}}}=\frac{1}{2}gt_{OB}^{2}\]                 we have \[{{t}_{OB}}=\sqrt{\frac{2{{h}_{OA}}}{g}}\] Given,   \[{{h}_{OB}}=80\,\,m,g=10\,\,m/{{s}^{2}}\] \[\therefore \] \[{{t}_{OB}}=\sqrt{\frac{2\times 80}{10}}=4\,s\] 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.