Motion In A Plane

Question

Wired Faculty App

A projectile is given an initial velocity of $\hat{i} + 2 \hat{j}$ The cartesian equation of its path is ( Take g= 10 ms² )

y = x $-$ 5x²

y = 2x $-$ 5x²

y = 2x $-$ 15 x²

y = 2x $-$ 25x²

Solution

y = 2x $-$ 5x²

Given:-

The initial velocity of a projectile is given by

$\vec{u} = \hat{i} + 2 \hat{j}$

= u_x $\hat{i}$ + u_y $\hat{j}$

Then,

u_x = 1 = u cosθ

u_y = 2 = u sinθ

∴ $tanθ = \frac{u sinθ}{u cosθ}$

= $\frac{2}{1}$

tanθ = 2

The equation of trajectory of a projectile motion is

y = x tanθ $- \frac{g x^{2}}{2 u^{2} \cos^{2} θ}$

= x tanθ $- \frac{g x^{2}}{2 {(u cosθ)}^{2}}$

∴ y = (x × 2 ) $- \frac{10 \times x^{2}}{2 {(1)}^{2}}$

y = 2x - 5x²

Some More Questions From Motion in A Plane Chapter

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.

For Daily Free Study Material Join wiredfaculty

Motion In A Plane

A projectile is given an initial velocity of $\hat{i} + 2 \hat{j}$ The cartesian equation of its path is ( Take g= 10 ms² )

y = x $-$ 5x²

y = 2x $-$ 5x²

y = 2x $-$ 15 x²

y = 2x $-$ 25x²

Some More Questions From Motion in A Plane Chapter

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.

What are polar vectors?

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Phone Number

Email Address

Loaction

For Daily Free Study Material Join wiredfaculty

Motion In A Plane

A projectile is given an initial velocity of i^ + 2 j^ The cartesian equation of its path is ( Take g= 10 ms2 ) y = x - 5x2 y = 2x - 5x2 y = 2x - 15 x2 y = 2x - 25x2

Some More Questions From Motion in A Plane Chapter

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.

What are polar vectors?

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

A projectile is given an initial velocity of $\hat{i} + 2 \hat{j}$ The cartesian equation of its path is ( Take g= 10 ms² )

y = x $-$ 5x²

y = 2x $-$ 5x²

y = 2x $-$ 15 x²

y = 2x $-$ 25x²

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.