A) 100 m
B) 200 m
C) 300 m
D) 400 m
Correct Answer: B
Solution :
Key Idea: At maximum height, final velocity is zero. From equation of motion, we have \[{{v}^{2}}={{u}^{2}}-2gh\] Where \[v\] is final velocity, \[u\] is initial velocity, \[h\] is height and \[g\] is acceleration due to gravity. Since body reaches maximum height in both cases, hence final velocity is zero. \[\therefore \] \[v=0\] \[\Rightarrow \] \[\frac{{{h}_{1}}}{{{h}_{2}}}=\frac{u_{1}^{2}}{u_{2}^{2}}\] Given, \[{{u}_{2}}=2{{u}_{1}},{{v}_{1}}=u\] \[\therefore \] \[\frac{{{h}_{1}}}{{{h}_{2}}}=\frac{{{u}^{2}}}{{{\left( 2u \right)}^{2}}}=\frac{1}{4}\] \[\Rightarrow \] \[{{h}_{2}}=4{{h}_{1}}=4\times 50=200\,m.\] Note: Maximum height attained does not depend upon the mass of the body.
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