A) \[b=\frac{a}{2}\]
B) \[b=a\]
C) \[b=2a\]
D) \[b=4a\]
Correct Answer: C
Solution :
The horizontal range (R) is given by \[R=\frac{{{u}^{2}}\sin 2\theta }{g}\] ?. (i) and \[H=\frac{{{u}^{2}}{{\sin }^{2}}\theta }{2g}\] ... (ii) Given, \[u=a\,\hat{i}+b\,\hat{j}={{u}_{x}}\,\hat{i}+{{u}_{y}}\,\hat{j}\] \[\therefore \] \[{{u}_{x}}=u\cos \theta =a\] ... (iii) \[{{u}_{y}}=u\sin \theta =b\] ... (iv) \[\therefore \] \[R=\frac{{{u}^{2}}(2\,\sin \theta )\,\,(\cos \theta )}{g}=\frac{2\,ab}{g}\] \[H=\frac{{{(u\sin \theta )}^{2}}}{2g}=\frac{{{b}^{2}}}{2\,g}\] Given, \[R=2\,H\] \[\frac{2\,ab}{g}=2\,\frac{{{b}^{2}}}{2\,g}\] \[\Rightarrow \] \[b=2\,a\]You need to login to perform this action.
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