# Horizontal Motion

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Horizontal Motion Definition

In physics, the projectile motion is broken into two components: horizontal and vertical. In most of the cases of projectile motion, the vertical component is due to the action of gravity.

For every object, the gravitational force causes a constant acceleration of 32.2 ft/s2 or 9.8 m/s2 towards the Earth.

Horizontal motion is defined as a projectile motion in a horizontal plane depending upon the force acting on it. For a short distance, the vertical and horizontal components of a projectile are perpendicular and independent of each other.

The horizontal component of speed of a projectile is constant throughout the flight duration. This is because, after launching the projectile, no horizontal force acts on it. So the projectile travels horizontally at a constant speed. To calculate the distance covered by a projectile, the following equation is used as,

Distance = speed × Time

d = vt

Horizontal Motion Physics

To obtain a horizontal motion, a projectile must be launched in a straight line, and not at any angle. The velocity of the projectile varies, but the direction in which a projectile is launched should be perpendicular to the surface of the Earth.

A constant vertical force of gravity acts upon the projectile which does not depend on the horizontal force, and is used to launch the projectile. This means that the total time of flight of the projectile will always be the same.

The projectile can be made to travel longer or shorter distances in the same amount of time by changing the initial velocity and the force applied to launch the projectile.

For long-distance travel, like that of a missile, a projectile must be launched at a particular angle, and the horizontal and vertical components must be determined to make the projectile travel a longer distance.

Motion in a plane is also called a motion in two dimensions. Some examples of two-dimensional motions are circular motion and projectile motion.

For the analysis of two-dimensional projectile motion, m is a reference point taken at the origin of two coordinate axes viz: X-axis and Y-axis. Projectile motion is one of the best examples of motion in a plane.

• The horizontal velocity of the ball remains constant while it falls because gravity doesn’t exert any horizontal force.

• As there is no force, the horizontal acceleration is zero (ax = 0)

• The ball moves in a steady state to the right at 5 m/sec

Horizontal Motion Examples

Some example of horizontal motion is given below:

• The motion of the Earth around the sun is horizontal.

• A boat traveling in a river.

• A shell fired from a gun.

• The motion of a billiard ball on the billiard table is horizontal.

• Throwing a ball or a cannonball is a horizontal motion.

Example of Horizontal Projectile Motion

Suppose, you want to calculate the time of flight and the distance traveled by a ball (projectile in this case) thrown from the top of Eiffel tower with a horizontal speed of 7 m/s.

1. First, launch the projectile at a horizontal speed of 7 m/s. Change the units if needed.

2. Calculate the initial height from which the motion of the projectile starts. The upper platform of Eiffel's tower is 276 m (906 ft) above the ground.

3. The calculator of horizontal projectile motion shows the tile of flight, distance traveled, and the trajectory.

It can be found out that it takes around 7 seconds for the ball to reach the surface or ground. The horizontal displacement will be approximately 48.56 m.

Remember that the tools of a horizontal projectile calculator are really flexible: just type any two known values in it and the horizontal projectile motion calculator will calculate the remaining parts.

For example, you can calculate the velocity required to throw a ball from the height, so that it reaches a horizontal distance of 100 m from the base of the tower.

Horizontal Motion Procedure

• Drop two stones vertically from the same height, and at the same time, one from each hand. Listen, when the stones hit the ground. They have to land on the surface ground at the same time.

• Repeat the same experiment, but this time, release one stones in a little horizontal motion by moving one of your hands sideways as you let the stones go.

• Repeat, and throw both the stones out sideways with different velocities.

• Try it with stones of unequal size.

• Try dropping both the stones from an open window or a staircase.

• Try to increase the horizontal speed of the stone.

• We could record the motion of the stones using a video camera.

Teaching Notes

• The objects of different masses, when launched with the same vertical acceleration, fall at the same time.

• The fall of a stone from a particular height takes the same time whether or not it has a horizontal motion.

• The independence of the horizontal component and vertical component of motion enabled Galileo to examine the horizontal motion of projectiles that are free from any accelerating force.

Q1. What are the Two Kinds of Projectile Motion?

Ans: There are two independent rectilinear motions:

i. Along x-axis: the axis of uniform velocity, which is responsible for the horizontal (forward) motion of the particle.

ii. Along y-axis: the axis of uniform acceleration, which is responsible for the vertical (downwards) motion of the particle.

Q2. In the Given Image Below, Jim Throws the Ball to the +X Direction with an Initial Velocity 10m/s. Time Gone While in Motion is 5s, Find Out the Height that the Object is Thrown, and Vy Component of the Velocity After it Falls to the Ground.

Ans:

In the vertical direction we have free fall motion:

h = ½(gt²) = ½ (10.5²)

h = 125 m

Vy = - gt

Vy = -10 m/s² × 5s

Vy = - 50 m/s

In horizontal direction, since the velocity is constant:

X = By

X = 10 m/s × 5 s

X = 50 m

Q3. What is the Formula for Horizontal Distance?

Ans: Horizontal distance is calculated by using the formula, X = V * t .

Vertical distance from the ground is calculated by the formula y = – g * t²/2.

Where,

g = acceleration due to gravity.

h = elevation.

Q4. How Far will the Ball Travel Horizontally?

Ans: If a ball is thrown horizontally at a velocity of 30 m/s, then after 1 second, it will have traveled 30 meters, and after 2 seconds it will have traveled 60 meters, after 3 seconds it will have traveled 90 meters, etc.

The distance traveled by the ball relies on the time.