A ball A is projected with speed $$50$$ $$ms-1$$ at an angle $$37o$$ with horizontal. At the same time, a second ball B is projected in a direction shown in the figure with speed $$60$$ $$ms-1$$ from a point $$91$$ m from A. Both ball collide in air. (Given$$, $$3$$ $$=$$ $$1.7) The value of θ isThe time when collision takes place is The distance of point of collision from initial position of A is

Question

A ball A is projected with speed $$50$$ $$ms-1$$ at an angle $$37o$$ with horizontal. At the same time, a second ball B is projected in a direction shown in the figure with speed $$60$$ $$ms-1$$ from a point $$91$$ m from A. Both ball collide in air. (Given$$, $$3$$ $$=$$ $$1.7) The value of θ isThe time when collision takes place is The distance of point of collision from initial position of A is

Infinity Learn · Accepted Answer

Since, both balls are at same levels, so for collision, $$vAY=vBYor$$ UAY−$$gt=UBY$$−gt∴ $$UAY=UBY$$⇒ $$50sin$$⁡$$37$$∘$$=60sin$$⁡θ⇒$$sin$$⁡θ$$=50$$×$$3560=12$$⇒ θ$$=30$$∘$$t=91uxrel$$ $$=9150cos$$⁡$$37$$∘$$+60cos$$⁡θ$$=9150$$×$$45+60$$×$$32=9191=1sxA=uAXt=40$$×$$1=40mand$$ $$yA=uAYt$$−$$12gt2=30$$×$$1$$−$$12$$×$$10$$×$$12=30$$−$$5=25$$∴ $$sA=xA2+yA2=402+252=47.17m$$

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