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Motion in A Plane

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Physics Part I

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Physics

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Class 10 Class 12
A person standing on a road has to hold his umbrella at 300 with the vertical to keep the rain away. He throws the umbrella and starts running at 10 m/s. He finds that raindrops are hitting his head vertically. Find the speed of raindrops with respect to, 

a) the road,
b) the moving person.

When a person is at rest with respect to ground, the rain is coming to him at an angle 30o with the vertical, i.e., along OB. 

As the person moves along OA with velocity 10 m/s, the relative velocity of rain w.r.t person is along OC as shown in fig. below.

                        

Here, o 

Therefore, velocity of rain w.r.t ground = straight v with rightwards harpoon with barb upwards on top subscript r g end subscript space equals space stack O B with rightwards harpoon with barb upwards on top 

Velocity of person w.r.t. ground = straight v with rightwards harpoon with barb upwards on top subscript p g end subscript space equals space stack O A with rightwards harpoon with barb upwards on top comma space w h e r e space O A space equals space 10 space m divided by s space equals space C B

Velocity of rain w.r.t person = straight v with rightwards harpoon with barb upwards on top subscript r p end subscript space equals space stack O C with rightwards harpoon with barb upwards on top 

a) increment OCB comma space OB space equals space CB divided by space sin space 30 to the power of 0

space space space space space space space space space space space space space space space space space space space space space equals space 10 divided by space left parenthesis 1 divided by 2 right parenthesis thin space equals space 20

Therefore comma space velocity space of space rain space straight w. straight r. straight t space ground space equals space 20 space straight m divided by straight s

b)

In increment space OCB comma space OB space equals space CB divided by tan space 30 to the power of straight o 

                          = 10/ (1/square root of 3) = 10square root of 3 

Therefore, velocity of train w.r.t person = 10square root of 3 m/s  

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What are the basic characteristics that a quantity must possess so that it may be a vector quantity?

A quantity must possess the direction and must follow the vector axioms. Any quantity that follows the vector axioms are classified as vectors. 


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