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Question

A particle is thrown with speed u at an angle of projection θ with horizontal as shown in figure. Choose the correct statement.

  1. Average velocity between A and C is ucosθ
  2. Dot product of vertical components of velocities at A and C is negative.
  3. All of these
  4. Average velocity between O and D is ucosθ


Solution

The correct option is C All of these
Between two points of equal height, the displacement will only be along the horizontal direction.x=ux×t  (where x is displacement and t is the time interval between two points of equal height.)
Average velocity =ux×tt=ucosθ    
Options (a) and (b) are correct. 
    As points A and C are at same height from the ground so, the magnitude of velocity will be same at both these points.    
    At point A, the vertical component of velocity is in upward direction as the particle is moving upwards in that direction. 
    At point C, the vertical component of velocity is in downward direction as the particle is moving downwards in that direction.       
As the vertical components of velocities at points A and C are in opposite direction to each other so their dot product is negative.
 

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