What Is The Initial Horizontal Velocity Of A Projectile: How to Find, Examples

In this post on physics, let us study the concept of what is the initial horizontal velocity of a projectile and its examples.

Whenever any projectile is released from its state of rest, it gains some velocity that helps it to move forward. The starting velocity that is gained by the projectile on its horizontal path is termed as initial horizontal velocity and can be found using the formulas that are mentioned below,

vix = vx – + 1/2axt

 vix = vfx – axt

vix2 = vfx2 – 2axx

 vix = vx /cosθ

Before studying in detail about what is the initial horizontal velocity of a projectile, let us know about projectile motion.

Projectile Motion: Concept and features

Projectile motion is one of the essential types of motion that is an essential part of mechanical physics.

When any object is thrown into open space, it travels along a trajectory that makes a shape of the parabolic curve under the influence of only gravitational force. This projectile motion is a particular case because the motion takes place in both the x and y component of a coordinate axis.

what is the horizontal velocity of a projectile

It’s time to know the main focus of this article: the initial horizontal velocity of a projectile.

What is the initial horizontal velocity of a projectile?

The word-initial refers to the beginning or starting point; displacement, velocity, etc.

Here the initial horizontal velocity of a projectile indicates the velocity gained by the projectile as soon as it launches or releases from the state of rest into the earth’s atmospheric surface. A projectile gains this initial velocity along the horizontal straight path. Hence it is given the name initial horizontal velocity of projectile motion.

vixt = vx – + 1/2axt

 vix = vfx – axt

 vix2 = vfx2 – 2axx

 vix = vx /cosΘ

Now take a peek into how to find the initial horizontal velocity of any projectile.

How to find the initial horizontal velocity of a projectile?

We can easily and quickly measure the value of initial horizontal velocity by noticing the formula to calculate a projectile’s horizontal velocity.

We have already known the formulas used to calculate horizontal velocity; consider those formulas and rearrange them so that you get you to get initial horizontal velocity as the main component to be measured. See below; we have arranged for them to get Vix.

Let us know these formulas elaborately by knowing the different approaches of what is the initial horizontal velocity of a projectile.

Different approaches to find what is the initial horizontal velocity of a projectile

The different approaches of what is the initial horizontal velocity of a projectile are as given as follows,

  • The first approach is to use the kinematics equation of mechanical physics to find out the initial horizontal velocity of a projectile.
  • The second approach is to look into the formulas used to measure the value of the horizontal velocity of a projectile.

We have to make some minor modifications to the initial velocity as the main component to be measured in both these approaches.

How does the initial velocity of a projectile affect its range?

There is an influence of the initial velocity of any projectile in some motion on its range.

We have to note down the three main factors that tell about the influence of initial velocity on the range. The main three factors are given below.

  • If the initial velocity Vix is more then, even the range of the projectile that is under the same motion will reach a greater height., In contrast, if the initial velocity is less, even the range will be limited.
  • Depending on whether the initial velocity is greater or lesser, the angle of the horizontal component of velocity varies.
  • Suppose we take any two projectiles launched at different angles, having different horizontal velocities into consideration. In that case, the range may be identical for the projectiles, but it reaches different maximum heights.

After knowing the influence of Vix on its range, let us study the method to find initial horizontal velocity in projectile motion.

How to find initial velocity in projectile motion?

One can find initial velocity in any projectile motion by using the below formulas,

Here if you are finding on different components of projectile motion, take into account the x or y component in place of velocity in the following formulas,

vixt = vx – + 1/2axt

 vix = vfx – axt

 vix2 = vfx2 – 2axx

Therefore, it will become easy to calculate the initial velocity by knowing these formulas. By solving some fundamental problems on what is the initial horizontal velocity of a projectile, we can study it better.

Problems based on the initial horizontal velocity of a projectile

Here are some problems based on the initial velocity of a projectile to better understand the concept.

Problem 1

A pack of garbage is thrown into the bin. The horizontal velocity is 25m/s, and the launching angle of the pack of garbage is 12°. Now find out the value of the initial horizontal velocity?

Solution: Let us first note down the given data,

The velocity along the horizontal path = Vx = 25m/s and θ = 12°

Now we can use one of the formulas as mentioned in the above concepts to measure initial horizontal velocity

Vix = Vx / Cos θ

Vix = (25) /Cos (12°)

Vix = 29.65m/s

Therefore, the required initial horizontal velocity is 29.65m/s

Problem 2

A single coin is thrown into the earth’s atmosphere. The horizontal velocity will be almost equal to 29m/s, and the angle of the coin when it is thrown is 20°. Now measure the initial horizontal velocity of the coin?

Solution: Let us first note down the given data,

The velocity along the horizontal path = Vx = 29m/s and θ = 20°

Now we can use one of the formulas as mentioned in the above concepts to measure initial horizontal velocity

Vix = Vx / Cos θ

Vix = (29)/ Cos (20°)

Vix = 30.88m/s

Therefore, the required initial horizontal velocity is 30.88m/s

What are the different examples of the initial horizontal velocity of a projectile in real life?

There are many examples that we find around us that will be a great example of the initial horizontal velocity of any projectile.

Every motion of a projectile occurs with gaining of velocity known to be initial velocity. When thrown above apart from a straight angle, all the material makes a parabolic curve while reaching the ground. So, we can consider the below-mentioned examples for initial horizontal velocity.

Long jump

Before taking a long jump, the athlete warms up their body then begins the motion. Here the component required for a long jump includes initial velocity. If the initial velocity is more than that, the long jump taken by the athlete will be higher.

what is the initial horizontal velocity of a projectile
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Running of horses

We have seen the running of horses may be in real or in any wildlife channels. If you notice carefully, while running, horses’ legs make a trajectory path. At the beginning of motion, the velocity present to initiate is known to be initial horizontal velocity.

Discus throw

Even in the game of discus throw, while throwing a disc, the velocity possessed by the disc along the horizontal path is initial horizontal velocity. If the velocity is more, even the disc will reach a greater height, increasing the chance of winning the game.

Throwing of basketball into the net

Even if we observe the basketball game, we can identify the parabolic path made by the player while making sure the ball enters the net. It is an example of projectile motion and even an example for initial horizontal velocity because the velocity as soon as the ball is thrown possessed by it.

Fireworks

We make sure that we lit fireworks and enjoy ourselves during the festival or any celebration. The velocity gained by the firework as soon as it lits termed to be initial horizontal velocity that influences the range of the fireworks to reach a certain point in the atmosphere. If the V is more, then, obviously, the fireworks reach maximum height.

Therefore, we can notice the projectile motion mainly in sports.

What factors tell initial velocity to affect the maximum height of a projectile?

Initial velocity directly influences the point of maximum height in a projectile motion.

If the speed of initial velocity is more, then the angle at which it is launched will be steeper. If this angle is increased, then there is a possibility that the maximum height in a projectile motion will increase. Therefore, we can infer that the change in initial velocity affects the maximum height of the projectile.

In this way, initial velocity and maximum height act based on each other.

Why does increasing initial velocity increase range?

The increasing initial horizontal velocity tends to increase the range of a projectile.

The term increasing initial horizontal velocity signifies that the position of a projectile with the time increase makes the projectile in motion move to a different height. These phenomena directly make the projectile a more extended height, increasing the projectile‘s range.

So, there is a direct effect of initial horizontal velocity on the range and maximum height of any projectile.

To study more:

Frequently Asked Questions | FAQs

What are the three main things affected by the initial horizontal velocity of a projectile motion?

The main factors that are affected by the initial horizontal velocity are

  • Projectile angle
  • Maximum height
  • Range of a projectile motion

What are the best examples of the initial horizontal velocity of a projectile motion?

The best examples of initial horizontal velocity are as below,

  • Waterfall
  • Jumping from a certain height or any vehicle
  • Baseball game
  • Launching of rockets
  • Falling of meteoroids.
  • Throwing any waste into the dustbin.
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