Motion In A Plane

Question

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A stone projected with a velocity u at an angle 0 with the horizontal reaches maximum height H,. When it is projected with velocity u at an angle $(\frac{π}{2} - θ)$ with the horizontal, it reaches maximum height H₂. The relation between the horizontal range R of the projectile, H₁ and H₂ is

R = $4 \sqrt{H_{1} H_{2}}$

R = 4 ( H₁ - H₂ )

R = 4( H₁ + H₂ )

R = $\frac{H_{1}^{2}}{H_{2}^{2}}$

Solution

R = $4 \sqrt{H_{1} H_{2}}$

We know that,

Maximum height of projectile equation is given by

H= $\frac{u^{2} \sin^{2} θ}{2 g}$

Where u = velocity of stone

θ = angle

H = maximum height

H₁ = $\frac{u^{2} \sin^{2} θ}{2 g}$

and H₂ = $\frac{u^{2} \sin^{2} (90 - θ)}{2 g}$

since H₁H₂ = $\frac{u^{2} \sin^{2} θ}{2 g} \times \frac{u^{2} \cos^{2} θ}{2 g}$

= $\frac{4}{4} \times \frac{u^{2} \sin^{2} θ}{2 g} \times \frac{u^{2} \cos^{2} θ}{2 g}$

H₁H₂= $\frac{{(u^{2} \sin 2 θ)}^{2}}{16 g^{2}}$

[ since sin²θ = 2 sinθ cosθ ]

H₁H₂ = $\frac{R^{2}}{16}$

R² = 16H₁ H₂

R = 4 $\sqrt{H_{1} H_{2}}$

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.