Velocity in certain direction[components]

[anigeo]

could you please tell me why the velocity of the block M along the horizontal direction is v/sinθ and not vsinθ as in the case of components of vectors?

 

[Doc Al]

could you please tell me why the velocity of the block M along the horizontal direction is v/sinθ and not vsinθ as in the case of components of vectors?

If I understand your diagram (the block is being dragged by the string along the surface), v is the rate at which the string is being pulled. To relate the speed of the block along the surface to the rate at which the string moves, consider the right triangle formed by the block and the string. Let x be the horizontal distance from block to pulley and z be the length of string between block and pulley. How can you relate those quantities?

 

[anigeo]

ok i understand what u say. actually this is also what i thought.so thanks.
but while taking the component of a vector along a direction θ from it we write vcosθ if v is the vector.why is it not applicable here?

 

[Doc Al]

but while taking the component of a vector along a direction θ from it we write vcosθ if v is the vector.why is it not applicable here?

The block moves along the horizontal. It's the component of the block's velocity (V_B) in the direction of the string that must equal the rate at which the string is pulled:
V_B sinθ = v

 

[PJC01]

The velocity of a block M along a certain direction is determined by its magnitude and direction. In this case, the magnitude of the velocity is represented by v and the direction is represented by θ. The formula v/sinθ represents the component of the velocity in the horizontal direction, while vsinθ represents the magnitude of the horizontal component of the velocity.

This difference arises because the component of a vector is the projection of the vector onto a specific direction. In this case, the horizontal component of the velocity is the projection of the overall velocity onto the horizontal direction. This projection is given by the formula v/sinθ, which takes into account the angle θ between the overall velocity and the horizontal direction.

On the other hand, vsinθ represents the magnitude of the horizontal component of the velocity, without considering the angle θ. This is why it is used in the case of components of vectors, where the focus is on the magnitude of the component rather than the direction.

In summary, the use of v/sinθ or vsinθ in the formula for the horizontal component of velocity depends on the context in which it is being used. When considering the overall velocity in a certain direction, v/sinθ is used to represent the component in that direction, while vsinθ is used when only the magnitude of the component is of interest.