A ball is projected at an angle of 30 ° above with the horizontal...

A ball is projected at an angle of

30 °

above with the horizontal from the top of a tower and strikes the ground in

5s

at an angle of

45 °

with the horizontal. Find the speed with which it was projected. A ball is projected at an angle of 30 ° above with the horizontal from the top of a tower and strikes the ground in 5s

A ball is projected at an angle of 30 ° above with the horizontal from the top of a tower and strikes the ground in 5s

Options

A $50\left(\sqrt{3} - 1\right){m s}^{- 1}$
B $50\left(\sqrt{2} - 1\right){m s}^{- 1}$
C $70\left(\sqrt{3} - 1\right){m s}^{- 1}$
D $80\left(\sqrt{3} - 1\right){m s}^{- 1}$

Correct answer

A. $50\left(\sqrt{3} - 1\right){m s}^{- 1}$

Step-by-step solution

{v}_{x} = - {v}_{y}

ucos30 ° = - ( usin30 ° - gt )

u\dfrac{3}{2} = - \left(\dfrac{u}{2} -

10 \times5\right)

<br /><br />u \left(\dfrac{\sqrt{3} + 1}{2}\right) =50

⇒ u =

100\left(\dfrac{1}{\sqrt{3} + 1}\right)⇒ u =

50\left(\sqrt{3} -1\right){m~s}^{- 1}

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