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Physics-

General

Easy

Question

A man standing on a hill top projects a stone horizontally with speed $v subscript 0 end subscript$ as shown in figure. Taking the coordinate system as given in the figure. The coordinates of the point where the stone will hit the hill surface

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

The correct answer is: $open parentheses fraction numerator 2 v subscript 0 end subscript superscript 2 end superscript t a n theta over denominator g end fraction comma fraction numerator negative 2 v subscript 0 end subscript superscript 2 end superscript tan to the power of 2 end exponent invisible function application theta over denominator g end fraction close parentheses$

Range of the projectile on an inclined plane (down the plane) is,
$R equals fraction numerator u to the power of 2 end exponent over denominator g c o s to the power of 2 end exponent beta end fraction left square bracket sin invisible function application open parentheses 2 alpha plus beta close parentheses plus sin invisible function application beta right square bracket$
Here, $u equals v subscript 0 end subscript comma alpha equals 0$ and $beta equals theta$
$therefore R equals fraction numerator 2 v subscript 0 end subscript superscript 2 end superscript sin invisible function application theta over denominator g cos to the power of 2 end exponent invisible function application theta end fraction$

Now $x equals R cos invisible function application theta equals fraction numerator 2 v subscript 0 end subscript superscript 2 end superscript tan invisible function application theta over denominator g end fraction$
and $y equals negative R sin invisible function application theta equals blank minus fraction numerator 2 v subscript 0 end subscript superscript 2 end superscript tan to the power of 2 end exponent invisible function application theta over denominator g end fraction$

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