What Is The Horizontal Velocity Of A Projectile: Different Aspects And Facts

The horizontal velocity is considered to occur along the x-axis. In this post, let us study about what is the horizontal velocity of a projectile.

The horizontal velocity(vx) of any projectile is the primary component of the body undergoing projectile motion. It is generally used to know the velocity value at which the particle travels along the horizontal path in any projectile motion. It is even considered the initial path covered by the body in motion.

To know the different aspects and facts of the horizontal velocity of a projectile, let us move further in this post.

What is the horizontal velocity of a projectile at its highest point?

As soon as the projectile reaches its highest point, it is attracted by gravitation force and moves downwards.

Suppose the particle in projectile motion reaches its highest point along the horizontal path. In that case, the horizontal velocity will usually be zero because as soon as it reaches the peak point, it is made to fall vertically downwards by the influence of the force of gravity. This horizontal velocity at its highest point does not encounter any influence from vertical velocity.

So, from this, we can infer that horizontal velocity will become zero whenever it reaches its highest point in a projectile motion. Now let us look into the fact of what is the horizontal velocity of a projectile and its formula.

what is the horizontal velocity of a projectile
Image: Horizontal velocity of a projectile

The horizontal velocity of a projectile formula

We have studied earlier how to find velocity in a motion; similarly, we can consider one of the methods of calculating velocity by taking into account displacement and time to calculate horizontal velocity.

  • The following formula helps measure the horizontal velocity of the projectile; we can either use the kinematics equation or only the initial velocity and launch angle to measure the horizontal velocity.
  • The kinematics equation includes displacement, acceleration, time, initial and final velocities.

                                                            Vx = Vi Cos θ

                                                            x = vixt + 1/2axt2

                                                            vfx = vix + axt

                                                            vfx2 = vix2 + 2axx

These are some crucial formulas that help measure the horizontal velocity. This concept helps in knowing what the horizontal velocity of the projectile is

The horizontal velocity of a projectile at its maximum height

As soon as the particle in projectile motion along the horizontal path reaches its maximum height, it will be constant.

The horizontal velocity in a projectile is usually measured in Vx. It will be constant until it reaches hmax; only the vertical velocity will be zero at the point of hmax, and later it undergoes variation due to gravity.

what is the horizontal velocity of a projectile
Image: Horizontal velocity at its maximum height

 Now to study in detail the calculation of maximum height.

How to find the horizontal velocity at maximum height?

The maximum height of a projectile along the horizontal path gains horizontal velocity, and it is calculated using the formula as shown below,

hmax = (VY)2 / 2g

Here

hmax refers to a maximum height

VY refers to vertical velocity

g refers to gravitational force

The above equation depicts the calculation of maximum height at the launching of the projectile. It only comes under the influence of the vertical vector component of the velocity at the beginning.

The horizontal velocity of a projectile launched at an angle

When thrown into open-air, every particle undergoes projectile motion and makes a certain angle while moving down towards the ground.

We know that the nature of the path in a projectile motion is parabolic in shape. When thrown, it moves with initial constant horizontal velocity and makes an angle θ as it reaches its maximum height. This angle is considered the launch angle of a projectile along the horizontal path.

Image: Horizontal velocity and angle of projectile

At this point of the post, let us go in-depth to know more facts about what is the horizontal velocity of a projectile at the peak of travel.

What is the horizontal velocity of a projectile at the peak of travel?

The peak of travel in a horizontal component of a projectile also refers to the maximum height attained by a projectile.

As we have studied in the above concepts, the velocity component along the vertical displacement will be zero at the maximum height. It becomes a horizontal component entirely at the point of hmax in the parabolic path. We can infer that as the velocity will be only along the horizontal path, the horizontal velocity will be zero at the travel peak.

To know more about the vertical velocity of a projectile motion, let us study the next concept.

What is the effect on the horizontal velocity in motion as it falls?

As soon as the projectile falls, it will be no more in the state of horizontal displacement, and hence there will be the absence of horizontal velocity.

  • There will be the absence of influence of gravitational force along the horizontal path; hence the horizontal velocity will maintain its constant velocity.
  • As the velocity will be constant, there will be not much change in acceleration. When it falls after reaching hmax, the horizontal part is now entirely vertical, and at this point, the influence of gravity acts on it.
  • Both the components will be independent of one another.

After knowing the components of the horizontal velocity of a projectile, let us study the variation in horizontal velocity at different launch angles.

What is the horizontal velocity of a projectile thrown at an angle of 60?

We know how to measure horizontal velocity with having the values of displacement, initial velocity, time and launch angle. But in this particular question, they have mentioned only the launch angle.

In the earlier concepts, we have come across that the horizontal velocity of a projectile will be along with the horizontal displacement of a projectile thrown at a certain angle and forms a trajectory; it is represented in the horizontal x-axis of velocity.

We can calculate horizontal velocity b=of a projectile that is thrown at an angle of 60 by considering the below equation,

                                                            Vx = Vi Cos θ

Here we can consider the value of θ as 60, focussing the horizontal direction then we can substitute the value of the angle in the above equation as shown,

                                                             Vx = Vi Cos 60

From trigonometric values, we can know the values of cos60 as ½ or 0.5

                                                             Vx = 1/2 Vi

Therefore, from the above substitution, we can conclude that when a projectile is thrown in the horizontal direction at an angle of 60, the obtained horizontal velocity will be half of the total projectile velocity.

Let us about more changes in horizontal velocity.

Can the horizontal velocity of a projectile change?

The horizontal velocity of any projectile motion does not change.

In any projectile motion, the horizontal component of velocity will remain constant until it reaches its certain height and only in the vertical direction it undergoes variation.

Therefore, we can infer that the velocity of a projectile in a horizontal direction does not change.

How does the horizontal velocity of a projectile become zero?

The horizontal velocity cannot be zero but will be constant throughout the motion.

When the initiation of a projectile motion takes place, it reaches a particular point called maximum height; till that point, the velocity remains constant as there will be no other force, and here the vertical velocity component will be zero.

what is the horizontal velocity of a projectile
Image Credit: Pixabay free images

So, from these facts, we can come to the theory that only the vertical component of velocity in a projectile motion will be zero, and anyway, the horizontal component of velocity will always be constant; that is, it maintains the value of initial velocity.

Why will the horizontal component of a projectile velocity be constant?

The horizontal component of the velocity that is considered in the projectile motion can be considered shortly as horizontal velocity.

The horizontal velocity is constant throughout the projectile motion because no other external force acts on the body in motion. It is the reason why gravity only influences the vertical component and not on the horizontal that makes the horizontal velocity component remain constant.

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Frequently Asked Questions | FAQs

What do you mean by maximum height in projectile motion?

The maximum height in a projectile motion is nothing but the highest point a projectile reaches during the movement.

  • Usually, we observe that when any material or object is thrown above, it goes up to a certain height and then travels back towards us due to the influence of gravitation.
  • The particular height a body reaches will be considered as the maximum height. At this point, there will be zero velocity, and the vertical motion of the body begins. Here, the initial velocity is applied to take the body along some height of horizontal path, known as the projectile range.

What is the relationship between a projectile motion’s horizontal and vertical velocity?

Both components of a projectile motion never depend on each other.

  • We have already known that any projectile motion consists of a horizontal and vertical velocity.
  • These two components are considered because projectile motion takes place in two-dimension.
  • The horizontal velocity component of the projectile motion has differed entirely in terms of nature and forces from the vertical component of the velocity vector of the body undergoing projectile motion.
  • As the name suggests, both the velocities occur along respective x and y coordinates.
  • Since they occur in different directions, they are independent of each other.
  • There is no specific relationship between horizontal velocity and vertical velocity.

Define the relation between horizontal velocity and maximum height?

There is no particular relationship between horizontal velocity and maximum height, but there is a specific relation between horizontal displacement and maximum height.

The displacement along the horizontal path simultaneously includes horizontal velocity. The displacement in the horizontal path is also termed its range; even this range influences the horizontal velocity. It is given a special formula as given below,

                                            h/R = tanθ/4

Here, there is an increase in angle, even the maximum height increases.

What do you mean by a range of a projectile?

The range of a projectile is usually influenced by horizontal velocity or speed.

The range is a unique name given to the distance travelled by a projectile along the horizontal direction. There will be no effect of acceleration along this path since, in a projectile, the only force of action that occurs is the gravitational force. This range is calculated by an essential formula that is mentioned below,

R = v02sin2θ/g

  • R indicates the horizontal range (m) of a projectile
  • Vo indicates the initial velocity (m/s) of a projectile
  • g indicates acceleration due to gravity that is experienced by a projectile
  • θ indicates the angle of the initial velocity from the horizontal plane

What is the relation between horizontal velocity and the range of a projectile?

The relation between horizontal velocity and the range of a projectile is determined by the horizontal path along which the particle moves in trajectory.

The maximum height of any projectile motion is a specific point at which some change in velocity occurs and where the vertical velocity of the projectile will always be zero. From this position, the projectile will take a curve to move downwards. We can notice that the horizontal velocity will remain the same until the body reaches a maximum height where the horizontal component will be zero and influences its range.

How do you find horizontal velocity with maximum height?

Horizontal velocity can be measured by considering various components such as maximum height, range and launch angle.

To know more about how to measure horizontal velocity and to know what is the horizontal velocity of the projectile, we have one formula that is useful in finding the horizontal velocity.

Hmax = (Vi)2 Sin2θi /g

Here initial velocity and the launched angle is taken into consideration.

How will the horizontal component of velocity for a projectile be affected by the vertical component Quizlet?

The vertical component of projectile velocity won’t affect its horizontal component.

Both horizontal and vertical velocity are the two main components of projectile velocity and will act perpendicularly to one another. At the same time, it’s in the perpendicular direction; both the components are not under the influence of one another.

What happens to the horizontal velocity in motion as it moves up?

As soon as the projectile starts to move up, it reaches a certain height, takes diversion, and begins to move vertically.

  • There will be no acceleration component that acts on the horizontal path that tends to make the horizontal velocity maintain its constant phase throughout its displacement. After reaching its max. Height and an acceleration amount of 9.8m/s act on the body attracted by gravity.
  • From this observation, we can imply that only the vertical velocity varies by an acceleration of 9.8m/s, whereas on the horizontal path, its velocity remains constant throughout its range.

Why does the horizontal velocity do not change during its flight?

The horizontal velocity in projectile motion does not change during its flight because no gravitational force acts on it.

We have studied in our earlier classes that for any change in velocity, there must be some gravitational force that acts on it. Keeping this concept in mind, if we see the nature of horizontal velocity, we know that the acceleration component is absent along the horizontal path; due to this, no gravity acts on it, leading to the absence of horizontal forces. All these factors contribute to maintaining the constant phase of horizontal velocity during its flight.

Why is horizontal velocity constant in a projectile motion?

The horizontal velocity is constant in a projectile motion due to the absence of change in acceleration along its horizontal path.

  • We can consider both horizontal velocity and the velocity at the initiation of a projectile motion identical. As the name suggests, the projectile travels through a horizontal straight path. We can notice the horizontal speed and velocity. This velocity will maintain a constant phase until it reaches a certain height, and the acceleration due to gravity only occurs on the vertical path and not on the horizontal.
  • We can sum up it since the acceleration is constant or absent throughout the horizontal displacement, and the horizontal velocity will be constant.

Why does horizontal velocity does not affect vertical velocity?

When anybody or object is thrown above, it gains velocity to move further.

  • In a projectile motion, as soon as trajectory occurs, the beginning initial velocity along the projectile’s parabolic path is considered horizontal velocity. At some point, the object reaches a certain height called maximum height. It is made to travel downwards as it gets attracted by the gravitational force. It is the one and the only force that acts in the projectile motion of any particle.
  • As soon as the particle moves below, a vertical displacement and velocity occur. Here both the horizontal and vertical velocities are opposite each other, and hence there will be no effect on horizontal velocity due to vertical velocity.

Mention the relationship between launched angle, maximum height and range of horizontal velocity?

The angle of maximum height increases as there will be an increase in horizontal range.

We have already studied no direct relation between horizontal velocity and range. If the projectile thrown at a certain angle reaches its maximum height, let us assume that the length will be comparably maximum, then even the range will be maximum. But as soon as the projectile moves vertically, the horizontal velocity will be zero.

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