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Relative Velocity in 2D

A cart is mov...

Question

A cart is moving horizontally along a straight line with constant speed $30 {ms}^{- 1}$ . A particle is to be fired vertically upwards from the moving cart in such a way that it returns to the cart at the same point from where it was projected after the cart has moved $80 m$ . At what speed (relative to the must the projectile be fired? (Take $g = 10 {ms}^{- 2}$ )

10 {ms}^{- 1}

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10 \sqrt{8} {ms}^{- 1}

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\frac{40}{3} {ms}^{- 1}

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none of these

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Solution

The correct option is C $\frac{40}{3} {ms}^{- 1}$

Let the projectile be fired at speed $v$ vertically w.r.t. cart.
Initial horizontal velocity of projectile
$u_{x} = u = 30 m/s$ and
$u_{y} = v$

Time taken for vertical journey = Time taken for horizontal journey = Time of flight $(T)$

$\Rightarrow \frac{2 v}{g} = \frac{x}{u_{x}} = \frac{80}{30}$
$∴ v = \frac{80 \times 10}{30 \times 2} = \frac{40}{3} m/s$

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