Motion In A Plane

Question

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What is the radius of curvature of the parabola traced out by the projectile in the previous problem at a point where the particle velocity makes an angle $\frac{θ}{2}$ with the horizontal?

$r = \frac{v^{2} \cos^{2} θ}{g \cos^{2} \frac{θ}{2}}$

$r = \frac{2 v sinθ}{g tanθ}$

$r = \frac{v cosθ}{g \sin^{2} \frac{θ}{2}}$

$r = \frac{3 v \cos θ}{g \cot θ}$

Solution

$r = \frac{v^{2} \cos^{2} θ}{g \cos^{2} \frac{θ}{2}}$

Let v be the velocity at the point where it makes an $\frac{θ}{2}$ angle with the horizontal.

The horizontal component remains unchanged. So

v_m $\cos (\frac{θ}{2})$ = u cosθ

⇒ v = $\frac{u cosθ}{\cos (\frac{θ}{2})}$ .....(i)

From figure

mg cos $(\frac{θ}{2}) = \frac{m v^{2}}{r}$

r = $\frac{v^{2}}{g \cos \frac{θ}{2}}$

Putting the value of v from Eq (i), we get

r = $\frac{v^{2} \cos^{2} θ}{g \cos^{2} \frac{θ}{2}}$

Some More Questions From Motion in A Plane Chapter

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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Motion In A Plane

Some More Questions From Motion in A Plane Chapter

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.

What are polar vectors?

Give two examples of polar vectors.

What are axial vectors?

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Entrance Exams Preparation

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Motion In A Plane

What is the radius of curvature of the parabola traced out by the projectile in the previous problem at a point where the particle velocity makes an angle θ2 with the horizontal? r = v2 cos2θg cos2 θ2 r = 2 v sinθg tanθ r =v cosθg sin2θ2 r = 3v cos θg cot θ

Some More Questions From Motion in A Plane Chapter

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.

What are polar vectors?

Give two examples of polar vectors.

What are 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.