Question

Figure shows four paths for a kicked football. Ignoring the effects of air on the flight, rank the paths according to initial horizontal velocity component keeping highest first.

Moderate

Solution

$R = \frac{u^{2} \sin 2 θ}{g} = \frac{2 u_{x} u_{y}}{g}$
$∴$ Range $\propto$ Horizontal initial velocity component (u_x) In path 4, range is maximum, so football has maximum horizontal velocity component in this path and in path 1, range is minimum. So, horizontal velocity component is minimum.

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