A) \[\frac{\hat{i}-2.2\,\hat{j}}{2.42}\]
B) \[\frac{-\,\hat{i}+1.3\,\hat{j}}{1.64}\]
C) \[\frac{\hat{j}+\,\hat{k}}{\sqrt{2}}\]
D) None of these
Correct Answer: B
Solution :
\[x=2-0.25\,{{t}^{2}}\] \[\therefore \,\,\,\,\,\,\,\,\,\,\,\,\,{{v}_{x}}=\frac{dx}{dt}=\,\,-\,0.5\,t\] and \[\operatorname{y} =\,\,t+\,\,0.025 {{t}^{2}}\] \[{{v}_{\operatorname{y}}} =\,\,\frac{dy}{dt}=1+\,\,0.075 {{t}^{2}}\] \[{{\operatorname{v}}_{x/t=2}}=\,\,-1\,m\,/s,\,{{v}_{y/t\,=\,2}}\,\,=\,\,1.3\,\,m/s\] \[\therefore ~~v=\,\,v\times \hat{i}\,\,+\,\,{{v}_{y}}\,\hat{j}\,\,=\,\,-\,\hat{i}\,\,+\,\,1.3 \hat{j}\] \[\hat{v}=\frac{v}{\left| v \right|}=\frac{(-\hat{i}+1.3\hat{j})}{1.64}\]
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