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A particle is projected with velocity u,making an angle x with horizontal, such that it touches four points of regular hexagon of side length H,find the value of x.

A particle is projected with velocity u,making an angle x with horizontal, such that it touches four points of regular hexagon of side length H,find the value of x.

Grade:12

1 Answers

Badiuddin askIITians.ismu Expert
147 Points
11 years ago

Dear Sudip

 

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dear to ensure that it passes through 4 point it is sufficient to proof that it passses through A and B and C is the maximum point of parabola

by symmetry it will also passe through the rest two point shown in figure

now co ordinate of A(R/2-H,H√3/2)

co ordinate of point B(R/2-H/2 ,H√3)

where R is the range of parabola

now we know

Y=Xtanx -gX2/2u2cosx

now put above two point two equation will form

subtract both equation.

and you can get the value of x



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