A rectangular billiard table has vertices at $$P0$$,$$0$$ , $$Q0$$,$$7$$, $$R10$$,$$7$$, and $$S10$$,$$0$$. A small billiard ball starts at $$M3$$,$$4moves$$ in a straight line to the top $$M3$$,$$4$$, moves in a straight line to the top of the table, bounces to the right side of the table, and then comes to rest at $$N7$$,$$1$$. The $$y-coordinate$$ of the point where it is the right side is

Question

A rectangular billiard table has vertices at $$P0$$,$$0$$ , $$Q0$$,$$7$$, $$R10$$,$$7$$, and $$S10$$,$$0$$. A small billiard ball starts at $$M3$$,$$4moves$$ in a straight line to the top $$M3$$,$$4$$, moves in a straight line to the top of the table, bounces to the right side of the table, and then comes to rest at $$N7$$,$$1$$. The $$y-coordinate$$ of the point where it is the right side is

Infinity Learn · Accepted Answer

$$tan$$θ$$=a$$−$$13=7$$−$$a10$$−bAlso, $$tan$$θ$$=7$$−$$4b$$−$$3=3b$$−$$3Hence$$, $$3b$$−$$3=a$$−$$13=7$$−$$a10$$−bFrom the first two relations, we have $$9=ab$$−b−$$3a+3or$$ $$3a+6=ab$$−b              (1)From$$ the last two relations, we have $$10a$$−ab−$$10+b=21$$−$$3aor$$ $$13a$$−$$ab+b=31or$$ ab−$$a=13a$$−$$31$$         $$(2$$ $$)Hence$$, from $$(1) and (2),$$3a+6=13a$$−$$31or$$  $$10a=37or$$ $$a=3.7$$

Start JEE / NEET / Foundation preparation at rupees 99/day !!

Detailed Solution

Get Expert Academic Guidance – Connect with a Counselor Today!