School Projectile Motion Problem

AI Thread Summary
To determine when a particle in projectile motion moves at a right angle to its previous direction, the discussion focuses on using both vector analysis and geometric principles. The key insight provided is that the time at which this occurs can be expressed as ucosec(θ)/g, aligning with vector solutions. The conversation emphasizes the importance of understanding slopes in relation to the tangent lines of the parabolic path. A reminder is given that the slope of a line perpendicular to another can be derived from the negative reciprocal of the original slope. The thread ultimately seeks clarity on the geometric approach to solving the problem.
jaysinghrath
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If a point of the parabolic path the velocity be u and the inclination to the horizon be θ, at what time the particle is moving at right angle to its former direction.
I was trying to solve it using vectors.
My friend gave me a clue of applying some geometry to the parabolic path given below:-
attachment.php?attachmentid=63307&stc=1&d=1382802353.jpg

He is definite that he solver it and the answer is = ucosec(θ)/g which is matching with the answer solving via vectors. Now he is not in contact, I was trying to solve this question.
PLZ help me
 

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If you recall your functions classes, a line perpendicular to a line with slope m has slope - 1/m. What 's the slope of the line tangent to the first point on your diagram? So what should be the slope of the second point?

Can you write another expression for the slope at the second point?
 

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