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An automobile traveling 95 km /h overtakes a 1.10-km- long train traveling in the same direction on a track parallel to the road. If the train’s speed is 75 km/h, how long does it take the car to pass it, and how far will the car have traveled in this time? See Fig. 2-39. What are the results if the car and train are traveling in opposite directions?

Respuesta :

Answer: a) 5.5 hours and 412.5 km b) 38 minutes and 47.5 km.

Step-by-step explanation:

Since we have given that

Speed of an automobile = 95 km /hr

Speed of train = 75 km/hr

Length of train = 110 km

If the train and automobile is travelling in the same direction, then the relative speed would be

95-75 = 20 km/hr

So, time taken by the car to pass it would be

[tex]\dfrac{110}{20}\\\\=5.5\ hours[/tex]

Car have traveled in 5.5 hours is given by

[tex]5.5\times 75\\\\=412.5\ km[/tex]

Similarly, if they are travelling in opposite directions, then the relative speed would be

[tex]95+75=170\ km\hr[/tex]

So, time taken by the car have traveled this time would be

[tex]\dfrac{110}{170}\\\\=0.64\ hours\\\\\approx 38\ minutes[/tex]

Car have traveled in 38 minutes is given by

[tex]\dfrac{38}{60}\times 75\\\\=47.5\ km[/tex]

Hence, a) 5.5 hours and 412.5 km b) 38 minutes and 47.5 km.

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