Question
A particle is projected from a point O with a velocity u in a direction making an angle α upward with the horizontal. After some time at point P it is moving at right angle with its initial direction of projection. The time of flight from O to P is
Answer: Option B
:
B
When body projected with initial velocity ⃗u by making angle α with the horizontal. Then after time t, (at point P) it’s direction is perpendicular to ⃗u
Magnitude of velocity at point P is given by v = ucotα (from sample problem no. 9)
For vertical motion : Initial velocity (at point O) =usinα
Final velocity (at point P) =−vcosα=−ucotαcosα
Time of flight (from point O to P) = t
Applying first equation of motion v=u−gt
−ucotαcosα=usinα−gt∴t=usinα+ucotαcosαg=ugsinα[sin2α+cos2α]=ucosecαg
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:
B
When body projected with initial velocity ⃗u by making angle α with the horizontal. Then after time t, (at point P) it’s direction is perpendicular to ⃗u
Magnitude of velocity at point P is given by v = ucotα (from sample problem no. 9)
For vertical motion : Initial velocity (at point O) =usinα
Final velocity (at point P) =−vcosα=−ucotαcosα
Time of flight (from point O to P) = t
Applying first equation of motion v=u−gt
−ucotαcosα=usinα−gt∴t=usinα+ucotαcosαg=ugsinα[sin2α+cos2α]=ucosecαg
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