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A train moves northwards with speed 80 ...

A train moves northwards with speed `80 km h^(-1)` . While a car moves towards east with a speed of ` 60 km h^(-1)` , what is the velocity of the train w.r.t the driver of the car ?

Text Solution

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Let us choose the x-y co-ordinates as given below .
Then the velocity of train and car are `barv_(tau) = 80 hatj, barv_(c ) = 60 hati`
Velocity of train w.r.t. the driver of the car
`bar(tauc) = barv_(tau)-barv_(c ) `
`bar(tauc) = 80 hatj-60hatj`
`= 80 hatj+(-60) hatj`
`:. |barv_(tauc)|=sqrt(v_(tau)^(2)+v_(c)^(2))`
`= sqrt(6400+3600)`
`|barv_(tauc)|=100 km//h`
Direction of `barv_(tauc)` in terms of angle `theta` which it makes with x-axis.

`tan theta =(v_(taucy))/(v_(taucx)) = (80)/(60)`
`theta = tan^(-1) ((4)/(3))`
So to the car driver the train appears to move with speed 100 m `s^(-1)` in the direction `tan^(-1)((4)/(3))` north of west .
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