A) \[\frac{1}{3}\hat{j}\,m{{s}^{-2}}\]
B) \[3\hat{j}\,m{{s}^{-2}}\]
C) \[\frac{2}{3}\hat{j}\,m{{s}^{-2}}\]
D) \[2\hat{j}\,m{{s}^{-2}}\]
Correct Answer: D
Solution :
Give equation is: \[y=9{{x}^{2}}\] Since, x-component of velocity remains constant, we have \[\frac{dx}{dt}=\frac{1}{3}\,m{{s}^{-1}}\] ?(i) From eq. (i) we have y-component of velocity \[\frac{dy}{dt}\,=18x.\,\frac{dx}{dt}\] \[\frac{{{d}^{2}}y}{d{{t}^{2}}}\,=18{{\left( \frac{dx}{dt} \right)}^{2}}=18{{\left( \frac{1}{3} \right)}^{2}}=2m{{s}^{-2}}\] \[{{a}_{y}}=2\hat{j}\,m{{s}^{-2}}\]
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