Two trains, each `50 m` long, are travelling in opposite directions with velocities `10 ms^-1 and 15 ms^-1`. The time of their crossing each other is.

Answer

4

Explanation

`y=x tan theta-(9x^(2))/(2u^(2) cos^(2) theta)`
`10=40 tan theta-(10xx1600(1+tan^(2) theta))/(2xx900)`
`10=40 tan theta-80/9-80/9 tan^(2) theta`
`8/9 tan^(2) theta-4 tan theta+17/9=0`
`8 tan^(2) theta-36 tan theta+17=0`
`tan alpha+tan beta=36/8`
`tan alpha+tan beta=17/8`
`tan (alpha+beta)=(tan alpha+tan beta)/(1-tan alpha tan beta)`
`=(36//8)/(1-17/8)=(36//8)/(-9//8)=-4`
So `|tan(alpha+beta)|=|-4|=4`