A truck is moving with a constant velocity of $54 km/h$ . In which direction (angle with the direction of motion of truck) should a stone be projected up with a velocity of $20 m/s$ relative to truck, so that for a person standing on the earth stone appears to be at right angles to the truck ?

{cos}^{- 1} (- \frac{3}{4})

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{cos}^{- 1} (- \frac{1}{4})

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{cos}^{- 1} (\frac{2}{3})

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{cos}^{- 1} (- \frac{4}{3})

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Solution

The correct option is A ${cos}^{- 1} (- \frac{3}{4})$
Let the stone be projected at an angle $α$ to the direction of motion of truck with a speed of $v = 20 m/s$ .
Since the resultant displacement along horizontal is zero.

The velocity along horizontal = 0
$15 + 20 cos α = 0 \Rightarrow cos α = - \frac{3}{4}$
$\Rightarrow α = {cos}^{- 1} (- \frac{3}{4})$

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