Question

(b) Shows that the projection angle θ₀for a projectile launched from the origin is given by,

$straight theta subscript straight o space equals space tan to the power of negative 1 end exponent open parentheses space fraction numerator 4 straight h subscript straight m over denominator straight R end fraction close parentheses$ ,

where the symbols have their usual meaning.

Solution

Maximum space vertical space height. space straight h subscript straight m space equals fraction numerator space straight u subscript 0 squared space Sin squared straight theta space over denominator space 2 straight g end fraction space space space space space space space... space left parenthesis straight i right parenthesis Horizontal space Range comma space straight R space equals space fraction numerator straight u subscript 0 to the power of 2 space end exponent Sin squared 2 straight theta space over denominator space straight g end fraction space space space space space space space space space space space space space... space left parenthesis ii right parenthesis fraction numerator straight h subscript straight m space over denominator straight R end fraction equals space fraction numerator Sin squared straight theta space over denominator 2 Sin squared 2 straight theta end fraction space space space space space space space space space equals space fraction numerator Sin space straight theta space cross times space Sin space straight theta space over denominator 2 space cross times 2 SinθCosθ end fraction space space space space space space space space equals space fraction numerator sin space straight theta over denominator 4 space Cosθ end fraction space equals space tan space straight theta over 4 rightwards double arrow space tan space straight theta space equals space left parenthesis fraction numerator 4 hm over denominator straight R end fraction right parenthesis rightwards double arrow space space straight theta space equals space tan to the power of negative 1 end exponent space open parentheses fraction numerator 4 hm over denominator straight R end fraction close parentheses

Some More Questions From Motion in A Plane Chapter

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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Motion In A Plane

Some More Questions From Motion in A Plane Chapter

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.

What are polar vectors?

Give two examples of polar vectors.

What are axial vectors?

Give two examples of axial vectors.

What are tensors?

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

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Motion In A Plane

(b) Shows that the projection angle θ0 for a projectile launched from the origin is given by,, where the symbols have their usual meaning.

Some More Questions From Motion in A Plane Chapter

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.

What are polar vectors?

Give two examples of polar vectors.

What are axial vectors?

Give two examples of axial vectors.

What are tensors?

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.