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A particle A is projected with an initia...

A particle A is projected with an initial velocity of 60 m/s. at an angle `30^(@)` to the horizontal. At the same time a second particle B is projected in opposite direction with initial speed of 50 m/s from a point at a distance of 100 m from A. If the particles collide in air, find (a) the angle of projection `prop` of particle B,

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Taking x and y directions as shown in figure.

Here, `veca_A=-ghatj," "bara_B=-ghatj`
`u_(ax)=60cos30^(@)=30sqrt3m//s`
`u_(ay)=60sin30^(@)=30m//s`
`u_(BX)=-50cosprop`
and `u_(ay)=50sinprop`
Relative acceleration between the two is zero as `a_A-a_B` . Hence, the relative motion between the two is uniform. It can be assumed that B is at rest and A is moving with `baru_(AB)`. Hence, the two particles will collide, if `baru_(AB)` is along AB. This is possible only when
`u_(ay)=u_(By)`
i.e., component of relative velocity along y-axis should be zero.
or `30=50 sin prop`
`:. prop=sin^(-1)(3//5)`
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