Two particles are projected simultaneously from the level ground as shown in the figure. They may collide after a time

\frac{x sin θ_{2}}{u_{1}}

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\frac{x cos θ_{2}}{u_{2}}

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\frac{x sin θ_{2}}{u_{1} sin (θ_{2} - θ_{1})}

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\frac{x sin θ_{2}}{u_{2} sin (θ_{2} - θ_{1})}

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Solution

The correct option is C $\frac{x sin θ_{2}}{u_{1} sin (θ_{2} - θ_{1})}$
$t = \frac{x}{u_{1} cos θ_{1} - u_{2} cos θ_{2}} . . . . . . . ⎛ ⎜ ⎝ 1 ⎞ ⎟ ⎠ A n d, u_{1} sin θ_{1} . t - \frac{1}{2} g t^{2} = u_{2} sin θ_{2} . t - \frac{1}{2} g t^{2} ∴ u_{1} sin θ_{1} = u_{2} sin θ_{2} . . . . . . . ⎛ ⎜ ⎝ 2 ⎞ ⎟ ⎠ f r o m ⎛ ⎜ ⎝ 1 ⎞ ⎟ ⎠ a n d ⎛ ⎜ ⎝ 2 ⎞ ⎟ ⎠ t = \frac{x}{u_{1} cos θ_{1} - \frac{u_{1} sin θ_{1} . cos θ_{2}}{sin θ_{2}}} ∴ t = \frac{x sin θ_{2}}{u_{1} sin (θ_{2} - θ_{1})}$

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Similar questions

A

B

t = 0

t = 0

g = 10 {ms}^{- 2}

g = 10 {ms}^{- 2}

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