Motion In A Plane : Motion In 2 Dimensions

Projectile Motion- Motion in a plane

We have learned about motion in a straight line and the three equations of motion. Now we will learn about motion in a plane. When we are talking about motion in plane, we are actually talking about motion in two dimensions, since two dimensions make a plane. So we are taking two axes in consideration, generally X-axis and Y-axis. In order to derive equations of motion in a plane we need to know about motion in one dimension.

The equations of motion in a straight line are:

\( v\) = \( u + at\)

\( s \) = \(ut + \frac{1}{2}at^{2}\)

\( v^2 \)=\( u^2 + 2as \)

Where,

v = final velocity of the particle

u = initial velocity of the particle

s = displacement of the particle

a = acceleration of the particle

t = time interval in which the particle is in consideration

In a plane, we have to apply the same equations separately in both the directions: Y axis and Y-axis. This would give us the equations for motion in a plane.

\( v_y\) = \( u_y + a_y t\)

\( s_y \) = \( u_y t + \frac{1}{2}a_y t^{2}\)

\( v_y^2 \) = \( u_y^2 + 2a_y s\)

Where,

vy = final velocity of the particle in y direction

uy = initial velocity of the particle in y direction

sy = displacement of the particle in y direction

ay = acceleration of the particle in y direction

t = time interval in which the particle is in consideration

Similarly, for X-axis:

\(V_x\) = \(u_x + a_x t\)

\(S_x\) =\( u_x t + \frac{1}{2}a_x t^{2}\)

\(V_x^2\) =\( u_x^2 + 2a_x s\)

Where,

vx = final velocity of the particle in x direction

ux = initial velocity of the particle in x direction

sx = displacement of the particle in x direction

ax = acceleration of the particle in x direction

t = time interval in which the particle is in consideration

Watch this video to have a better and visual understanding of motion in a plane.

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Motion in a plane

The above diagram represents the motion of an object under the influence of gravity. It is an example of projectile motion (an special case of motion in a plane)

Projectile motion is one of the most common examples of motion in a plane. In a projectile motion, the only acceleration acting is in the vertical direction which is acceleration due to gravity (g). Therefore, equations of motion can be applied separately in X-axis and Y-axis to find the unknown parameters. To know more about projectile motion watch the video give below:

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Practise This Question

Ram goes from point A to B by auto at the speed of 20 km/hr and comes back from B to A in a cab at a speed of 80 km/hr. Find his average speed.