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Relative Velocity in 2D

Single Correc...

Question

Single Correct Answer Type
At what angle with the horizontal should a ball be thrown so that its range $R$ is related to the time of flight as $R = 5 T^{2}$ . Take $g = 10 m s^{- 2}$ :

30

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45

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60

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90

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Solution

The correct option is B $45$
$R = 5 T^{2}$
$\frac{v^{2} s i n 2 θ}{g} = 5 (\frac{2 v s i n θ}{g})^{2}$

$⟹ s i n 2 θ = \frac{20 s i n^{2} θ}{10} = 2 s i n^{2} θ$

$2 s i n θ c o s θ = 2 s i n^{2} θ$
$⟹ c o s θ = s i n θ$
$∴ θ = 45^{o}$

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