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ADNAN MUHAMMED

Grade 12,

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A particle is projected with velocity u at angle theta with horizontal find the time when velocity vector is perpendicular to intial velocity vector

A  particle is projected with velocity  u  at angle  theta  with horizontal find the time when velocity vector is perpendicular to intial velocity vector 

Grade:11

2 Answers

Eshan
askIITians Faculty 2095 Points
5 years ago
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Piyush Kumar Maurya
65 Points
5 years ago
Initial velocity = u
u = ux + uy
u = ucos theta i cap+ usin theta j cap
Here ux remains constant throughout the journey.
Velcity at time t = v
Vx = ucos theta 
Vy = usin theta - gt
V(t) = ucos theta i cap + (usin theta - gt) j cap
 
Now for V(t) to be perpendicular to u , their dot product should be zero.
 So , V(t) . u = 0
       [ ucos theta i cap + ( usin theta - gt) j cap] .               (ucos theta i cap + usin theta j cap) = 0 
> u2 cos^2 theta + u2 sin^2 theta - usin theta *gt = 0
 >  t= u / sin theta *g 

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