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Grade: 11
A projectile is projected from the ground at t=0 with initial speed u at angle theta with horizontal 
4 months ago

Answers : (1)

23769 Points

See we need to find the time at which initial velocity vector is perpendicular to velocity vector at that time , 

initially the angle is theta  ( I'm considering the angle as @ )

resolving initial velocity vector we get,   usin@j^ + ucos@i^

Now at any time t velocity vector of projectile is given by formula, 

V vector = ucos@i^ + (usin@ - gt)j^

We have initial and final required velocity vector, 

since it is given they are perpendicular their dot product must be 0 

⇒ u^2cos^2@ + u^2sin^2@ - gtusin@ = 0

= u^2 - gtusin@ = 0

⇒ t= u/gsin@

4 months ago
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