RAIN, UMBRELLA,AND VECTORS

First, we must know about relative velocity. Say, you are travelling in a express train at the speed of 100km/hour. In the next track another train is moving at the speed of 120km/hour. Now subtract your speed (100) from 120 km/hour. You get 20km/hour. That means, another train is running at the speed of just 20km/hour with respect to you. Hence it will apear to go slowly for you.

Say, rain is falling vertically at the speed of 4 kmph. Draw a 4 cm arrow pointing downwards. It is the vector representing rain's speed.
You are fast walking at the speed of 6 kmph towards east. Draw 6 cm arrow from the head of rain vector representing your speed. To find the relative velocity, we have to subtract. Hence reverse your vector (-6cm) towards west side. If we now add both the vectors, we will get the relative velocity.

To add, complete the triangle, the third side gives the result of addition.(triangular law of vector addition).The length of the third side is found to be 7.2 cm and it makes an angle 33.7 with the horizontal. It means, the rain is falling at the increased speed of 7.2 kmph slantingly at an angle 33.7 degrees in your view. When you run in the rain, it will splash in your face. If you hold the umbrella at the proper angle, you can save your face.
For the same reason, the rain falls slantingly across the train's glass window. Also the boat appears to go at an angle, when it crosses a flowing river.

This is the one use of vectors. When a quantity has a direction, we go for vectors. Geometry is the basis of vectors. But one can solve problems just using formulas.

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