Home
Class 12
PHYSICS
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

Verified by Experts

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 .
Promotional Banner

Similar Questions

Explore conceptually related problems

Two parallel rail tracks run north-south. On one track train A moves noth with a speed of 54 km h^(-1) and on the other track train B moves south with a speed of 90 km h^(-1) . The velocity of train A with respect to train B is

Two paarallel rail tracks run north-south Train A moves north with a speed of 54 km h^(-1) and train B moves south with a speed of 90 km h^(-1) . What is the a. relative velocity of B with respect to A ? b. relaity of a monkey running on the roof of the train A against its motion (with its velocity of 18 km h^(1) with respect ot the train A ) as observed by a man standing on the fround?

A bus appears to move northwards at a speed of 20sqrt3 " km h"^(-1) . To a man diving his car eastwards with speed 20 " km h "^(-1) . Find the velocity of the bus w.r.t ground.

A car moves with a speed of 80 km/hr . What is the speed of the car in metres per second?

A train is moving with a velocity 40 km h^(-1) due East and a car is moving with a velocity 60 km h^(-10 due North, What is the velocity of train as appears to a passenger in the car ?

the distance between two stations is 20 km. if a train moves with a constant speed of 60 km h^(-1) , then the time taken by the train moves with a constant speed of 60 km h^(-1) , then the time taken by the rain to reach the next station is _____

A car is moving towards east with a speed of 25 km h^-1 . To the driver of the car, a bus appears to move towards north with a speed of 25 sqrt(3) km h^-1 . What is the actual velocity of the bus ?

To a driver going east in a car with a velocity of 40 km h^(-1) , a bus appears to move towards north with a velocity of 40 sqrt(3)km h^(-1) . What is the actual velocity and direction of motion of the bus ?

The distance between two railwat stations A and B is 440 km. two trains T_(1) and T_(2) start simultaneously from the stations A and B , respectively , and move twards each other. Then train T_(1) and T_(2) start simultaneouslym from the station A and B respectively, and move towards each other. the train T_(1) moves with a constant speed of 60 km h^(-1) and the train T_(2) moves with a speed of 50 km h^(-1) , Determine the point where they meet and the time taken for this.