# Homework Help: How to interpret this projectile motion problem

1. Feb 1, 2004

### mcintyre_ie

Hey
I just need some help with intepreting this question. Ive allready solved the first part (A), but im not sure as to when the time t1 occurs. Heres the question:
(A) A particle is progected with speed u at an angle alpha to the horizontal. If the maximum height reached is the same as the total horizontal range, show that tan alpha = 4
(B) The particle moves at right angles to its original direction of motion after a time t1 and then strikes the horizontal plane after 8s, both times measured from the instant of projection.
Show u = g(root)17
Calculate t1

Ok, so ive shown tan alpha = 4 and u = g(root)17, but i dont know when t1 occurs. Is it when the maximum vertical height is achieved? Any help is appreciated.
Thanks in advance

2. Feb 1, 2004

### HallsofIvy

Draw a simple picture: a horizontal straight line and a second line at angle &alpha; to it. That second line represents the initial direction of velocity. Draw its horizontal and vertical components. They have length, of course, of u cos&alpha; and u sin&alpha; resepectively. Now at the end of the second line draw a third line perpendicular to the second. Also draw a vertical line from the point of intersection of second and third and complete the right triangle with a horizontal line.

That represents the velocity vector, with horizontal and vertical components, when "the projectile is moving at right angles to the initial trajectory". What is the angle at the top of this right triangle? You should be able to see that the two right triangles are congruent and comparing the horizontal and vertical components, that the horizontal component of velocity is now v sin&alpha; and the vertical component is -v cos&alpha; (v is the speed at t1. It is not the same as u!). You know that vx= u cos&alpha; and that -v cos&alpha;= u sin&alpha;- g t1. From those two equations you can find v and t1.

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