Two persons Ram and Shyam are throwing ball at each other as shown in the figure. The maximum horizontal distance from the building where Ram can stand and still throw a ball a Shyam is $$d1$$. The maximum horizontal distance of Ram from the building where Shyam can throw a ballis da. If both of them can throw ball with a velocity of $$2gh$$, find out the ratio of $$d22d12$$.Neglect the height of each person.

Question

Two persons Ram and Shyam are throwing ball at each other as shown in the figure. The maximum horizontal distance from the building where Ram can stand and still throw a ball a Shyam is $$d1$$. The maximum horizontal distance of Ram from the building where Shyam can throw a ballis da. If both of them can throw ball with a velocity of $$2gh$$, find out the ratio of $$d22d12$$.Neglect the height of each person.

Infinity Learn · Accepted Answer

$$y=xtan$$⁡θ−$$gx22u2sec2$$⁡θWhen Ram throws the ball,       $$h=xtan$$⁡θ−$$gx22(2gh)21+tan2$$⁡θ$$tan2$$⁡θ−$$8hxtan$$⁡θ$$+1+8h2x2=0For$$ real roots,              D≥$$0$$⇒$$8hx2$$−$$4(1$$    $$+8h2x22$$≥$$0$$⇒    x≤$$8h$$⇒    $$xmax=8h$$        $$d1=8hWhen$$ Shyam throws the ball,$$y=xtan$$⁡θ−$$gx22u2cos2$$⁡θ⇒ −$$h=xtan$$⁡θ−$$gx22(2gh)2sec2$$⁡θ⇒$$tan2$$⁡θ−$$8hxtan$$⁡θ$$+1$$−$$8h2x2=0For$$ real roots,          D≥$$0$$ $$8hx2$$−$$41$$−$$8h2x2$$≥$$0$$    x≤$$24h$$    $$xmax=24h$$   $$d2=24h$$   $$d22d12=24h8h2=3$$

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