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 siren’) 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:
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)=30*30`
`(AP)^2+32(AP)-900=0`
`AP=(-32pmsqrt(3^3+3600))/2`
`=(-32pm68)/2=36/2,-50`
AP=18km.
`OA=V_v*t`
`PA=V_c*t`
`V_c/V_v=(PA)/(AO)=18/30=3/5`.
`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)=30*30`
`AP^2+32AP-900=0`
`AP=(-32pmsqrt3^2+3600)/2“=(32pm68)/2=36/2,-50`
AP=18Km
`OA=V_v*t`
`pa=v_c*t`
`(v_c)/(v_v)=(PA)/(AO)=18/30=3/5`.