First slide

Projection Under uniform Acceleration

Question

A man standing on a hill top projects a stone horizontally with speed v₀ as shown in fig. (2). Taking the coordinate system as shown in figure, the
coordinates of the point where the stone will hit the hill surface will be

Moderate

A

$(\frac{2 v_{0}^{2} \tan θ}{g}, - \frac{2 v_{0}^{2} \tan^{2} θ}{g})$
B

$(\frac{2 v_{0}^{2}}{g}, \frac{2 v_{0}^{2} \tan^{2} θ}{g})$
C

$(\frac{2 {v_{0}}^{2} \tan θ}{g}, \frac{2 {v_{0}}^{2}}{g})$
D

$(\frac{2 v_{0}^{2} \tan^{2} θ}{g}, \frac{2 v_{0}^{2} \tan θ}{g})$

Solution

See fig.
The range of the projectile on an inclined plane is given by
$R = \frac{u^{2}}{{gcos}^{2} β} [\sin (2 α + β) + \sin β]$ (down the plane)
Here, $u = v_{0}, α = 0 and β = θ$
$∴ R = \frac{2 v_{0}^{2} \sin θ}{{gcos}^{2} θ}$
Now $X = Rcos θ = \frac{2 v_{0}^{2} \tan θ}{g}$
and $y = - Rsin θ = - \frac{2 v_{0}^{2} \tan^{2} θ}{g}$

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