Motion In A Plane

Question

A body is projected vertically upwards. The times corresponding to height h while ascending and while descending are t₁ and t₂, respectively.

$\frac{g \sqrt{t_{1} t_{2}}}{2}$

$\frac{g (t_{1} + t_{2})}{2}$

$g \sqrt{t_{1} t_{2}}$

$g \frac{t_{1} t_{2}}{(t_{1} + t_{2})}$

Solution

$\frac{g (t_{1} + t_{2})}{2}$

Let v be the initial velocity of vertical projection and t be time taken by the body to reach a height h from the ground.

Here u = u,

a = -g,

s = h,

t = t

Using,

$ut + \frac{1}{2} (- g) t^{2} or {gt}^{2} - 2 ut + 2 h = 0 ∴ t = \frac{2 u \pm \sqrt{4 u^{2} - 4 g x 2 h}}{2 g} = \frac{u \pm \sqrt{u^{2} - 2 gh}}{g} It means t has two values, i . e ., t_{1} = u + \frac{\sqrt{u^{2} - 2 gh}}{g} t_{2} = \frac{u - \sqrt{u^{2 -} 2 gh}}{g} t_{1} + t_{2} = \frac{2 u}{g} or u = \frac{g (t_{1} + t_{2})}{2}$

Some More Questions From Motion in A Plane Chapter

What is a vector quantity?

Give three examples of scalar quantities.

Give three examples of vector quantities.

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

A body is projected vertically upwards. The times corresponding to height h while ascending and while descending are t₁ and t₂, respectively.

$\frac{g \sqrt{t_{1} t_{2}}}{2}$

$\frac{g (t_{1} + t_{2})}{2}$

$g \sqrt{t_{1} t_{2}}$

$g \frac{t_{1} t_{2}}{(t_{1} + t_{2})}$

Some More Questions From Motion in A Plane Chapter

What is a vector quantity?

Give three examples of scalar quantities.

Give three examples of vector quantities.

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.

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

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Motion In A Plane

A body is projected vertically upwards. The times corresponding to height h while ascending and while descending are t1 and t2, respectively. gt1t22 g(t1 +t2)2 gt1t2 gt1t2(t1+t2)

Some More Questions From Motion in A Plane Chapter

What is a vector quantity?

Give three examples of scalar quantities.

Give three examples of vector quantities.

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.

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

A body is projected vertically upwards. The times corresponding to height h while ascending and while descending are t₁ and t₂, respectively.

$\frac{g \sqrt{t_{1} t_{2}}}{2}$

$\frac{g (t_{1} + t_{2})}{2}$

$g \sqrt{t_{1} t_{2}}$

$g \frac{t_{1} t_{2}}{(t_{1} + t_{2})}$

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.