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+32AP-900=0` `AP=(-32pmsqrt3^2+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`.