A)
B)
C)
D)
Correct Answer: C
Solution :
[C]| \[\vec{v}=a\hat{i}+bx\hat{j}\] | ||
| \[{{v}_{x}}=a\] and \[{{v}_{y}}=bx\] | ||
| \[\frac{dx}{dt}=a\] | ||
| \[\therefore x=at+C\] | ||
| Since \[x=0\] at \[t=0,\] \[c=0\] | ||
| \[\therefore x=at\] | ||
| \[\frac{dy}{dx}=bx=abt\] | ... (1) | |
| \[\therefore y=\frac{ab{{t}^{2}}}{2}+C\] | ||
| \[\therefore y=\frac{ab{{t}^{2}}}{2}\] | ||
| as \[y=0\]at \[t=0\] | ...(2) | |
| From equation (1) and (2), | ||
| \[y=\frac{ab{{t}^{2}}}{2}=\frac{b}{2a}{{x}^{2}}\] | ||
| Hence the trajectory is a parabola symmetrical about the y-axis. | ||
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