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Motion in A Plane

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Physics Part I

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Physics

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CBSE Gujarat Board Haryana Board

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Class 10 Class 12

A projectile is fired from the surface of the earth with a velocity of 5 m/s and angle straight theta with the horizontal. Another projectile fired from another planet with a velocity of 3 m/s at the same angle follows a trajectory which is identical with the trajectory of the projectile fired from the earth. The value of the acceleration due to gravity on the planet is,

  • 3.5

  • 5.9

  • 16.3

  • 110.8


A.

3.5

If the trajectory is same for both the projectiles, their maximum height will be the same.

That is,

(Hmax)1 = (Hmax)2

i.e., 
space space space space space space space space fraction numerator straight u subscript 1 squared space sin squared straight theta over denominator 2 straight g subscript 1 end fraction space equals space fraction numerator straight u subscript 2 squared space sin squared straight theta over denominator 2 straight g subscript 2 end fraction
rightwards double arrow space straight u subscript 1 squared over straight u subscript 2 squared space equals space straight g subscript 1 over straight g subscript 2
rightwards double arrow space fraction numerator left parenthesis 5 right parenthesis squared over denominator left parenthesis 3 right parenthesis squared end fraction space equals space fraction numerator 9.8 over denominator g subscript 2 end fraction
rightwards double arrow space g subscript 2 italic space italic equals italic space fraction numerator italic 9 italic. italic 8 italic space x italic space italic 9 over denominator italic 25 end fraction
italic space italic space italic space italic space italic space italic space italic space italic space italic space italic space italic equals italic space italic 3 italic. italic 5 italic space m italic divided by s to the power of italic 2

If the trajectory is same for both the projectiles, their maximum height will be the same.

That is,

(Hmax)1 = (Hmax)2

i.e., 
space space space space space space space space fraction numerator straight u subscript 1 squared space sin squared straight theta over denominator 2 straight g subscript 1 end fraction space equals space fraction numerator straight u subscript 2 squared space sin squared straight theta over denominator 2 straight g subscript 2 end fraction
rightwards double arrow space straight u subscript 1 squared over straight u subscript 2 squared space equals space straight g subscript 1 over straight g subscript 2
rightwards double arrow space fraction numerator left parenthesis 5 right parenthesis squared over denominator left parenthesis 3 right parenthesis squared end fraction space equals space fraction numerator 9.8 over denominator g subscript 2 end fraction
rightwards double arrow space g subscript 2 italic space italic equals italic space fraction numerator italic 9 italic. italic 8 italic space x italic space italic 9 over denominator italic 25 end fraction
italic space italic space italic space italic space italic space italic space italic space italic space italic space italic space italic equals italic space italic 3 italic. italic 5 italic space m italic divided by s to the power of italic 2

1750 Views

Give three examples of scalar quantities.

Mass, temperature and energy
769 Views

What is a scalar quantity?

A physical quantity that requires only magnitude for its complete specification is called a scalar quantity.
1212 Views

What is a vector quantity?

A physical quantity that requires direction along with magnitude, for its complete specification is called a vector quantity.
835 Views

Give three examples of vector quantities.

Force, impulse and momentum.
865 Views

What are the basic characteristics that a quantity must possess so that it may be a vector quantity?

A quantity must possess the direction and must follow the vector axioms. Any quantity that follows the vector axioms are classified as vectors. 


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