a car is going Eastwards with a velocity 8 metre per second. to the passengers in the car, a train appears to be moving northwards with a velocity 15 metre per second what is the actual velocity of the train

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Solution

$T h e r e l a t i v e s p e e d o f t h e t r a i n t o w a r d s n o r t h f r o m t h e d i r e c t i o n o f e a s t w a r d i s g i v e n 15 m / s, s o t h e r e a l s p e e d o f t r a i n i s, v^{2} = 15^{2} + 8^{2} = 225 + 64 = 289 o r v = 17 m / s a n d d i r e c t i o n i s, \cos θ = \frac{8}{17} = 0.4706 o r θ = \cos^{- 1} (0.4706) = 62 ° a p p r o x i m a t e l y f r o m t h e d i r e c t i o n o f c a r t o w a r d s n o r t h o f e a s t .$

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a car is going Eastwards with a velocity 8 metre per second. to the passengers in the car, a train appears to be moving northwards with a velocity 15 metre per second what is the actual velocity of the train

The relative speed of the train towards north from the direction of eastwardis given 15m/s, so the real speed of train is, v2=152+82=225+64 =289or v = 17m/sand direction is,cosθ =817=0.4706or θ=cos-10.4706=62° approximately from the direction of car towards north of east.