If one of the rectangular components of a velocity of 36m/s has
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If one of the rectangular components of a velocity of 36m/s has magnitude 26 m/s, then what is the magnitude of other rectangular component of velocity?


If  are the magnitudes of rectangular components of velocity vector of magnitude v, then

                   

Given,

                and      

∴               

           
That is,

               , is the magnitude of other rectangular component of velocity. 

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On the airport, the sunshines just over the head. When the aeroplane takes off at an angle of 23° to horizontal, the shadow moves along the track with velocity 240km/hr. Find the velocity with which the aeroplane moves away from the earth. (Take space tan space 23 degree space equals space 5 divided by 12)

The vertical component ofvelocity of the airplane will give us the velocity with which the airplane moves away from the Earth. 

As the aeroplane takes off at angle  with horizontal, 

 ∴            

∴                

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The vector is given by,

                         

The X, Y and Z components of the vector are, 

∴  ,,                   

So, the resultant of the vector is given by,

       

Thus, 

Direction cosine is, 

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A force inclined at angle 37° with the horizontal has vertical component 42N. Find the magnitude of force and magnitude of its horizontal component. (Take sin 37° = 0·6 and cos 37° = 0·8)

Let F be the magnitude of force.

If force vector subtends an angle θ with the horizontal, then horizontal and vertical components of force respectively, 

                   and     

Here,

Angle with which the force is inclined to the horizontal,

Vertical component of the force,  

So, magnitude of force is found using, 

∴               

Force, 

Horizontal component,             
       
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Find Z component of resultant of vectors,
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Resultant of 

      is the Z component of vector.

Therefore Z component of resultant of  is zero.

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