A ball is projected from point A with a velocity, 10ms^ - 1...

A ball is projected from point A with a velocity,

10ms^{- 1}

perpendicular to the inclined plane as shown in the figure. Range of the ball on the inclined plane is :

A ball is projected from point A with a velocity, 10ms^ - 1 perpendicular to the inclined plane as shown in the figure.

A ball is projected from point A with a velocity, 10ms^ - 1 perpendicular to the inclined plane as shown in the figure.

Options

A $\dfrac{4 0}{3} m$
B $\dfrac{2 0}{13} m$
C $\dfrac{13}{20} m$
D $\dfrac{13}{40} m$

Correct answer

A. $\dfrac{4 0}{3} m$

Step-by-step solution

\text{T} = \dfrac{{2u \sin 90}^{o}}{{g \cos 30}^{o}} = \dfrac{2 \text{u}}{\text{g} \text\cos 3 {0}^{o}}

\text{R} = \dfrac{1}{2} \times \left({g \sin 30}^{o}\right) \times \dfrac{4 u^{2}}{g^{2} \cos^{2} {30}^{o}}

\text{R} = \dfrac{2 u^{2} \times 4}{2 \times 1 0 \times 3} = \dfrac{2 \times 1 0 \times 1 0 \times 4}{2 \times 1 0 \times 3} = \dfrac{4 0}{3} m

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