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The horizontal and vertical displacements of a particle moving along a curved line are given by x=5t and y=2t2 +t. Time after which its velocity vector makes an angle of 45 degree with the horizontal is ---------

The horizontal and vertical displacements of a particle moving along a curved line are given by x=5t and y=2t2 +t. Time after which its velocity vector makes an angle of 45 degree with the horizontal is ---------

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Grade:12th pass

2 Answers

Arun
25750 Points
6 years ago
Dear Akash
 
As at an angle of 45° both the components i.e. horizontal and vertical components of velocity should be equal as 
Cos45 = sin 45
Hence
dx/dt = dy/dt
5 = 4t +1
4t = 4
t = 1 sec.
Hence after 1 sec, velocity vector will make an angle of 45°
Regards
Arun (askIITians forum expert)
RO
82 Points
6 years ago
 
Dear Akash
 
As at an angle of 45° both the components i.e. horizontal and vertical components of velocity should be equal as 
Cos45 = sin 45
Hence
dx/dt = dy/dt
5 = 4t +1
4t = 4
t = 1 sec.
Hence after 1 sec, velocity vector will make an angle of 45°

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