Medium
Shown are several curves [fig. $(a)$,$(b)$,$(c)$,$(d)$,$(e)$,$(f)$]. Explain with reason,which ones amongst them can be possible trajectories traced by a projectile (neglect air friction).
(C) According to Kepler's laws of planetary motion and Newton's law of gravitation,the trajectory of a particle moving under the influence of a central gravitational force (like that of the Earth) must be a conic section (ellipse,parabola,or hyperbola) with the center of the Earth as one of its foci.
$1$. Figure $(a)$ is not a conic section.
$2$. Figure $(b)$ does not have the Earth at a focus.
$3$. Figure $(c)$ shows an elliptical path with the Earth at one of its foci,which is a valid trajectory.
$4$. Figure $(d)$ is a spiral,which is not a conic section.
$5$. Figure $(e)$ does not have the Earth at a focus.
$6$. Figure $(f)$ is a complex path that does not represent a standard conic section.
Therefore,only figure $(c)$ represents a possible trajectory for a projectile.
$1$. Figure $(a)$ is not a conic section.
$2$. Figure $(b)$ does not have the Earth at a focus.
$3$. Figure $(c)$ shows an elliptical path with the Earth at one of its foci,which is a valid trajectory.
$4$. Figure $(d)$ is a spiral,which is not a conic section.
$5$. Figure $(e)$ does not have the Earth at a focus.
$6$. Figure $(f)$ is a complex path that does not represent a standard conic section.
Therefore,only figure $(c)$ represents a possible trajectory for a projectile.
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