From the top of a tower of height h, particle A is projected horizontally with speed u. Simultaneously, particle B is projected from the foot of the tower with speed v at angle θ above the horizontal, toward the same side.if the two particles collide in air, which relation must necessarily hold?
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Question

From the top of a tower of height h, particle A is projected horizontally with speed u. Simultaneously, particle B is projected from the foot of the tower with speed v at angle θ above the horizontal, toward the same side.if the two particles collide in air, which relation must necessarily hold?

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G1 Physics · Accepted Answer

Take the foot of the tower as origin. Particle A: x A x_A x A ​ = ut, y A y_A y A ​ = h - ½gt². Particle B: x B x_B x B ​ = v cosθ·t, y B y_B y B ​ = v sinθ·t - ½gt². At collision, x A x_A x A ​ = x B . x_B. x B ​ . For t>0, u = v cosθ. Thus, v cosθ = u is necessary. The vertical-coordinate condition gives the collision time: h = v sinθ·t, but it does not replace the necessary horizontal relation.