A) \[f\]is continuous but not differentiable
B) \[f\]is differentiable but not continuous
C) \[f\]is continuous and differentiable
D) None of the above
Correct Answer: A
Solution :
Let\[\alpha \]be the angle between the components u and v of the resultant velocity w. Then, \[{{w}^{2}}={{u}^{2}}+{{v}^{2}}+2uv\text{ }cos\alpha \] ...(i) But it is given that \[u=v=w\] \[\therefore \] \[{{u}^{2}}={{u}^{2}}+{{u}^{2}}+2{{u}^{2}}cos\,\alpha \] \[\Rightarrow \] \[2(1+\cos \alpha )=1\] \[\Rightarrow \] \[4{{\cos }^{2}}\frac{\alpha }{2}=1\] [using\[1+cos2\theta =2\text{ }co{{s}^{2}}\theta \]] \[\Rightarrow \] \[\cos \frac{\alpha }{2}=\frac{1}{2}\] \[\Rightarrow \] \[\frac{\alpha }{2}=60{}^\circ \] \[\Rightarrow \] \[\alpha =120{}^\circ \]
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