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Motion In Straight Line

Question
CBSEENPH11017130
Wired Faculty App

Two straight lines drawn on the same displacement time graph make angle 30° with each other as shown in the figure. For what value of straight theta velocity of A will be three times the velocity of B?

Solution
On analysing the given graph,
Velocity of the particle A is given by, 
straight v subscript straight A space equals space tan space left parenthesis straight theta plus 30 to the power of straight o right parenthesis space 
Velocity of particle B is given by, 
straight v subscript straight B space equals space tanθ 
Here, vA = 3 vB 
tan space left parenthesis theta space plus space 30 to the power of o right parenthesis space equals space 3 space tan space theta U sin g space t h e space f o r m u l a space o f space tan space left parenthesis A plus B right parenthesis comma space w e space h a v e space space space space fraction numerator tan space theta space plus space space tan space 30 to the power of 0 over denominator 1 space minus tan theta space tan space 30 to the power of o end fraction space equals space 3 space tan space theta rightwards double arrow space space tan theta space plus space tan 30 to the power of 0 space equals space 3 space tan theta space minus space 3 space tan squared theta space tan space 30 to the power of o space rightwards double arrow space space 3 space tan space 30 to the power of o space tan squared theta space minus space 2 space tan theta space plus space tan space 30 to the power of o space equals space 0 space rightwards double arrow space space space space space tan space theta space equals space fraction numerator 2 plus-or-minus square root of 4 space minus 12 space tan squared 30 to the power of o end root over denominator 6 space tan space 30 to the power of o end fraction S u b s t i t u t i n g space tan space 30 to the power of o space equals space fraction numerator 1 over denominator square root of 3 end fraction comma space w e space g e t space space space space space space space space tan space theta space equals space fraction numerator 1 over denominator square root of 3 end fraction space rightwards double arrow space space space space space space space space space space space space theta space equals space 30 to the power of o  
 
 

Some More Questions From Motion in Straight Line Chapter

What is rest?

What is motion?

Is absolute rest or absolute motion possible?

What is the most essential thing to study the motion of a body?

Can a body be always at rest in some frame?

Can a body be in motion in the frame associated with the body itself?

When an object in motion can be considered as particle or point object?

Can you think of physical phenomena involving the moon in which moon cannot be treated as particle?

A train is crossing the bridge. Can it be taken as a particle?

Can a train be taken a particle? Give an example in support of your answer.

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