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A particle has two equal acclerations in two given direction.If one of the acceleration is half then the angle which the resultan makes with the other is also half.The angle between the acceleration is???

A particle has two equal acclerations in two given direction.If one of the acceleration is half then the angle which the resultan makes with the other is also half.The angle between the acceleration is???

Grade:11

1 Answers

Priyansh Bajaj AskiitiansExpert-IITD
30 Points
11 years ago

Dear Banjit,

Let,'a' be the magnitude of acceleration, 'x' be the angle between accelerations, and 'y' be the angle between resultant and one of the acceleration.

Then, tan y = a sin x / (a + acos x)  [ Standard formula in vectors]

tany = sinx/ (1+ cos x)........................(1)

If 'a' becomes 'a/2' then 'y' becomes 'y/2'

So, tan(y/2) = (a/2) sin x / (a + (a/2) cosx)

tan (y/2) = sinx / (2+cos x)

Also, tany = 2tan(y/2) /(1 - tan2 (y/2) )

Putting value of tan(y/2) in above eq. will give-

tan y = 2sinx (2+ cos x) / (2cos2x + 4cos x + 3)...................(2)

On comparing eq. (1) and (2), we get-

2(1 + cosx) (2+ cos x)  =  (2cos2x + 4cos x + 3)

or, cos x = 1/2

or, x= 600 [ANS]

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All the best Banjit!!!

Regards,
Askiitians Experts
Priyansh Bajaj

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