__Question1:__ A train having length 600 meters crosses a car going in the same direction at a speed of 12 km/hr. in 45 seconds. The same train crosses another man going on bike in opposite direction to that of train in 20 seconds. Find the speed of the other man on bike in km/hr.?

**Solution:**

This is the case of moving object without length.

Let the speed of the train be ‘s’.

Since speed of the man in car = 12 km/hr. = 12⨯5/18 = 10/3 m/sec.

So,

negative sign means both the train and the car are moving in same direction

Now, let the speed of the bike be ‘s0’ m/sec.

positive sign is used here because both the train and the bike are going in opposite direction.

Now speed of bike in km/hr. = 40/3⨯18/5 = 48km/hr.

i) Going in the same direction.

ii) Going in opposite direction.

**Solution:**

Let the length of each train be ‘l’ meters and their let their speeds be ‘s1’ m/sec and ‘s2’ m/sec.

**i) Train going in same direction.**

**i) Train going in same direction.**

**Solution:**

Here we will not consider moving object with length rather we will go for moving object without length. Because the reference here is a person not the train in which he is sitting. Also the speed of that man will be considered equal to the speed of the train in which he is sitting.

So, speed of man = 60 km/hr. and time = 1.2 minutes = 12/10⨯60 = 72 seconds.

**Solution:**

Here there are two cases:

Case 1: When the person sitting in the train crosses the bridge. (t = 25sec)

This means it is the case of moving object with no length. Let the length of platform be ‘lp’. Then length of the bridge:

Since, Distance = speed⨯ time.

Case 1: When the person standing on the ground had seen train crossing the bridge. (t = 40sec).

Let the length of train be ‘l’ meters.

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