There is a tall building with cylindrical base standing in a horizontal smooth plane. Radius of the cylinder base of the building is R $$=$$ $$8$$ m. Two friends Ram and Shyam standing at points P and Q respectively, on opposite side of the building. Ram standing at P (at$$ a distance $$10$$ m from the centre of the cylindrical base of the $$building) knows that his friend Shyam is standing at Q behind the building. The line joining P and Q passes through the centre of the base of the building. Distance between P and Q is $$50$$ m. Ram wants to throw a ball to Shyam but he realises that the building is too tall and he cannot throw the ball over it. Ram throws the ball at a speed of $$20$$ $$m/s$$ such that his friend Shyam at Q has to move minimum distance to catch it. What is the minimum distance (in$$ $$meter) that Shyam standing at Q will have to move to catch the ball?

Question

There is a tall building with cylindrical base standing in a horizontal smooth plane. Radius of the cylinder base of the building is R $$=$$ $$8$$ m. Two friends Ram and Shyam standing at points P and Q respectively, on opposite side of the building. Ram standing at P (at$$ a distance $$10$$ m from the centre of the cylindrical base of the $$building) knows that his friend Shyam is standing at Q behind the building. The line joining P and Q passes through the centre of the base of the building. Distance between P and Q is $$50$$ m. Ram wants to throw a ball to Shyam but he realises that the building is too tall and he cannot throw the ball over it. Ram throws the ball at a speed of $$20$$ $$m/s$$ such that his friend Shyam at Q has to move minimum distance to catch it. What is the minimum distance (in$$ $$meter) that Shyam standing at Q will have to move to catch the ball?

Infinity Learn · Accepted Answer

In the figure, we can observe the top view of the situation. Ram will throw the ball so that it passes tangentially (just$$ $$missing) to the building. The ball can fall on line Pt at different locations for different angles of projection.Shyam standing at Q will have to move a minimum distance if the ball lands at N such that QN⊥Pt. In similar, triangles, △POM and Δ$$PQNlmin50=R10$$⇒$$lmin=810$$×$$50$$∴$$lmin=40m$$

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