There are two angles of projection for which horizontal range is same. Prove that the sum of maximum heights for these two angles is independent of angle of projection.

Solution

Given, horizontal range is same for two angles of projection.
The angles are θ and 90°–θ.
Maximum height H₁ for angle projection θ is,
$straight H subscript 1 equals fraction numerator straight u squared sin squared straight theta over denominator 2 straight g end fraction$
Maximum height H₂ for angle projection 90°–θ is,
$space space space space straight H subscript 2 equals fraction numerator straight u squared sin squared left parenthesis 90 degree minus straight theta right parenthesis over denominator 2 straight g end fraction equals fraction numerator straight u squared cos squared straight theta over denominator 2 straight g end fraction$

Now, sum of maximum height is,
$space space space space space straight H subscript 1 plus straight H subscript 2 equals fraction numerator straight u squared sin squared straight theta over denominator 2 straight g end fraction plus fraction numerator straight u squared cos squared straight theta over denominator 2 straight g end fraction equals fraction numerator straight u squared over denominator 2 straight g end fraction$

Hence the result.

Some More Questions From Motion in A Plane Chapter

Pick out the only vector quantities in the following list:
Temperature, pressure, impulse, time, power, total path length, energy, gravitational potential, coefficient of friction and charge.

Pick out the two scalar quantities in the following list:
force, angular momentum, work, current, linear momentum, electric field, average velocity, magnetic moment, reaction as per Newton’s third law, relative velocity.

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Motion In A Plane

There are two angles of projection for which horizontal range is same. Prove that the sum of maximum heights for these two angles is independent of angle of projection.

Some More Questions From Motion in A Plane Chapter

What is a vector quantity?

Give three examples of scalar quantities.

Give three examples of vector quantities.

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

Is a physical quantity, having a direction, necessarily a vector?

Name a quantity which is both scalar as well as vector.

Which of the followings is/are vector quantities: work, power, acceleration, mass, momentum?

Pick up the odd one from the following: force, linear momentum, mass, impulse.

Pick out the only vector quantities in the following list:
Temperature, pressure, impulse, time, power, total path length, energy, gravitational potential, coefficient of friction and charge.

Pick out the two scalar quantities in the following list:
force, angular momentum, work, current, linear momentum, electric field, average velocity, magnetic moment, reaction as per Newton’s third law, relative velocity.

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NCERT Sample Papers

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For Daily Free Study Material Join wiredfaculty

Motion In A Plane

There are two angles of projection for which horizontal range is same. Prove that the sum of maximum heights for these two angles is independent of angle of projection.

Some More Questions From Motion in A Plane Chapter

What is a vector quantity?

Give three examples of scalar quantities.

Give three examples of vector quantities.

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

Is a physical quantity, having a direction, necessarily a vector?

Name a quantity which is both scalar as well as vector.

Which of the followings is/are vector quantities: work, power, acceleration, mass, momentum?

Pick up the odd one from the following: force, linear momentum, mass, impulse.

Pick out the only vector quantities in the following list:Temperature, pressure, impulse, time, power, total path length, energy, gravitational potential, coefficient of friction and charge.

Pick out the two scalar quantities in the following list: force, angular momentum, work, current, linear momentum, electric field, average velocity, magnetic moment, reaction as per Newton’s third law, relative velocity.

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Pick out the only vector quantities in the following list:
Temperature, pressure, impulse, time, power, total path length, energy, gravitational potential, coefficient of friction and charge.

Pick out the two scalar quantities in the following list:
force, angular momentum, work, current, linear momentum, electric field, average velocity, magnetic moment, reaction as per Newton’s third law, relative velocity.