Two particles are projected simultaneously from the same point with velocities v1 and v2 at angles alpha and beta with the horizontal. If they collide in mid-air, what is the condition on their velocities and angles?

A. v_1 = v_2 — For collision, both particles must have the same horizontal displacement at any time t. Since they start from the same point, v1 cos(alpha) * t = v2 cos(beta) * t must hold for all t.

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$Two particles are projected simultaneously from the same point with velocities v_{1} and v_{2} at angles α and β with the horizontal. If they collide in mid-air, what is the condition on their velocities and angles?$

A. $v_{1} cos α = v_{2} cos β$
B. $v_{1} sin α = v_{2} sin β$
C. $v_{1} tan α = v_{2} tan β$
D. $\frac{v _{1}}{c o s α} = \frac{v _{2}}{c o s β}$

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Correct answer: A — $v_{1} cos α = v_{2} cos β$

Solution

For collision, the horizontal positions must be equal at time t, so v_{1} cos α t = v_{2} cos β t . This implies v_{1} cos α = v_{2} cos β .

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Two particles are projected simultaneously from the same point with velocities v1​ and v2​ at angles α and β with the horizontal. If they collide in mid-air, what is the condition on their velocities and angles?

Solution

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More Kinematics practice questions

$Two particles are projected simultaneously from the same point with velocities v_{1} and v_{2} at angles α and β with the horizontal. If they collide in mid-air, what is the condition on their velocities and angles?$