A) 5.8 km
B) 4.7 km
C) 3.3 km
D) 2.0 km
Correct Answer: C
Solution :
The velocity of plane in horizontal direction, \[{{v}_{x}}=600\,km{{h}^{-1}}=\frac{600\times 1000}{60\times 60}m{{s}^{-1}}=\frac{500}{3}m{{s}^{-1}}\] Due to inertia this is also the velocity of body which remains constant during the flight of body. Initial velocity of body in vertical direction\[{{U}_{y}}=0\]. If t is time taken by the body to reach the earth, then from relation \[s=ut+\frac{1}{2}a{{t}^{2}},\]we have \[h=\frac{1}{2}g{{t}^{2}}\]or\[t=\sqrt{\frac{2h}{g}}=\sqrt{\frac{2\times 1960}{9.8}}=20s\] \[\therefore \]Distance traversed by body in horizontal direction \[AB={{v}_{x}}t=\frac{500}{3}\times 20=\frac{10}{3}\times {{10}^{3}}m\]\[=3.3km\]
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