(a) Show that for a projectile the angle between the velocity and the x-axis as a function of time is given by,

$straight theta left parenthesis straight t right parenthesis thin space equals space tan to the power of negative 1 end exponent space open square brackets fraction numerator straight v subscript oy space minus space gt over denominator straight v subscript ox end fraction close square brackets$

Solution

Let v_0x and v_0y respectively be the initial components of the velocity of the projectile motion along horizontal (x) and vertical (y) directions.

Let v_x and v_y be the horizontal and vertical components of velocity at a point P respectively.
Time taken by the projectile to reach point P = t
Using the first equation of motion along the vertical and horizontal directions, we get
v_y = v_0y = gt, and
v_x = v_{0x
$therefore space tan space straight theta space equals space straight v subscript straight y over straight v subscript straight x space equals space fraction numerator open parentheses straight v subscript 0 subscript straight y space end subscript minus space gt close parentheses over denominator straight v subscript 0 straight x end subscript end fraction rightwards double arrow space straight theta space equals space tan to the power of negative 1 end exponent space open parentheses fraction numerator straight v subscript 0 subscript straight y space end subscript minus space gt over denominator straight v subscript 0 straight x end subscript end fraction close parentheses$}

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

Some More Questions From Motion in A Plane Chapter

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.

What are polar vectors?

Give two examples of polar vectors.

What are axial vectors?

Give two examples of axial vectors.

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

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Motion In A Plane

(a) Show that for a projectile the angle between the velocity and the x-axis as a function of time is given by,

Some More Questions From Motion in A Plane Chapter

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.

What are polar vectors?

Give two examples of polar vectors.

What are axial vectors?

Give two examples of axial vectors.

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.