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21 Dec 2007 01:34:02 IST

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projectile motion

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a projectile is thrown at ana angle of 40 degrees with the horizontal and its range is R1. another projectile is thrown at ana angle of 40 degrees with the vertical and its range is R2. what is the relation between R1 and R2?

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A K

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Joined: 21 Dec 2007

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21 Dec 2007 03:04:59 IST

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R1=2Uy/g.Ux where Ux is ucos

and Uy is u sin

while for R2 it is vice versa coz of 90-

therefore the ans is 1:1

Indzee ...

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21 Dec 2007 03:23:25 IST

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Re:projectile motion

Indzee ...

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Joined: 2 Dec 2007

Posts: 124

21 Dec 2007 03:24:41 IST

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There is a imp relation between R1 and R2 (complimentary angles wala), you will find that R1 = R2

As,

R1 = U² Sin2(40) /g

R2 = u² Sin2(50) /g

As, Sin2(50) = Sin2(40)....... {Bcoz Sin(90+10) = Sin (90-10)}

We have R1 = R2 (provided that U = u)

Look at the diagram if you have any confusion!

Bipin Dubey

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Joined: 23 Jan 2007

Posts: 7749

21 Dec 2007 09:05:01 IST

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Range is given by : R = u²sin2

/g

R₁ = u²sin(2x40)/g = u²sin80 / g

similarly R₂ = u²sin100 / g

now use sin

= sin(180-

)

so, sin100 = sin(180-100) = sin80

Hence R₁ = R₂

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