Motion In A Plane

Question

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Water level is maintained in a cylindrical vessel upto a fixed height H. The vessel is kept on a horizontal plane. At what height above the bottom should a hole be made in the vessel, so that the water stream coming out of the hole strikes the horizontal plane of the greatest distance from the vessel?

$h = \frac{H}{2}$

$h = \frac{3 H}{2}$

$h = \frac{2 H}{3}$

h = $\frac{3}{4} H$

Solution

$h = \frac{H}{2}$

In general

Below equation is obtained from Kinematic equation

v² = u² + 2ah

Instead of acceleration 'a' we used 'g'

The velocity with which water will came out

v = $\sqrt{2 g (H - h)}$

The time of flight of water ejected from the hole.

t = $\sqrt{\frac{2 h}{g}}$ = time of flight

∴ distance = velocity × time

⇒ x = v × t

= $\sqrt{2 g (H - h)}$ × $\sqrt{\frac{2 h}{g}}$

⇒ x = $\sqrt{4 (Hh - h^{2})}$

For x to be maximum

$\frac{dx}{dh} = 0$

⇒ d $\frac{\sqrt{h (Hh - h^{2})}}{dH}$ = 0

⇒ 0 = H - 2h

⇒ h = $\frac{H}{2}$

Some More Questions From Motion in A Plane Chapter

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

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?

Give one example of tensor.

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

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For Daily Free Study Material Join wiredfaculty

Motion In A Plane

Some More Questions From Motion in A Plane Chapter

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?

Give one example of tensor.

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.