A train enters into a tunnel AB at A and exits at B. A jackal is sitting at 0 in another by-passing tunnel AOB, which is connected to AB at A and B, where OA is perpendicular to OB. A cat s sitting at P inside the tunnel AB making the shortest possible distance between O and P, such that AO=30 km and PB=32 km. when a train before entering into the tunnel AB makes a whistle (or sirenâ€™) somewhere before A ,the Jackal and cat run towards A. they meet with accident with the train) at the entrance A. The ratio of speeds of jackal and cat is

A train enters into a tunnel AB at A and exits at B. A jackal is sitti

1.	A train enters into a tunnel AB at A and exits at B. A jackal is sitting at 0 in another by-passing tunnel AOB, which is connected to AB at A and B, where OA is perpendicular to OB. A cat s sitting at P inside the tunnel AB making the shortest possible distance between O and P, such that AO=30 km and PB=32 km. when a train before entering into the tunnel AB makes a whistle (or sirenâ€™) somewhere before A ,the Jackal and cat run towards A. they meet with accident with the train) at the entrance A. The ratio of speeds of jackal and cat is
Answer» OP`_\|_`AB AO=30km PB=32km `/_AOB=90^0` `/_OBA=theta` `tantheta=(OA)/(OB)=30/(OB)` `Sintheta=(OA)/(AB)=30/(AP+32)` `In/_APO` `Cos(90-theta)=(AP)/(AO)` `sintheta=(AB)/(30)-(2)` `(AP)/30=30/(AP+32)` `AP(AP+32)=3030` `(AP)^2+32(AP)-900=0` `AP=(-32pmsqrt(3^3+3600))/2` `=(-32pm68)/2=36/2,-50` AP=18km. `OA=V_vt` `PA=V_c*t` `V_c/V_v=(PA)/(AO)=18/30=3/5`.