In this post, we will study in detail the approaches of how to find the horizontal velocity of a projectile
We can find the horizontal component of a velocity in a projectile motion using the available kinematics equations. It gives the exact meaning of velocity, but here, the horizontal path is considered distance and divided by time. The formula used to find the horizontal velocity of a projectile is
- v_{fx}^{2} = v_{ix}^{2} + 2a_{x}x
- v_{fx} = v_{ix} + a_{x}t
- v_{x} = cosΘ
Now let us see the various approaches and problems on how to find the horizontal velocity of a projectile.
How to find horizontal velocity of a projectile?
The projectile motion of anybody or an object is considered as a horizontal velocity; it can be measured using the kinematics equations of motion.
One of the basic formulas to find the horizontal velocity is to divide the horizontal distance traveled by a projectile along the considered path with the time taken.
Now let us study the facts of projectile motion.
Projectile motion: Concept and Facts
In physical science, the motion of a projectile is a type of two-dimensional motion that takes place along a parabolic path.
The only force that influences a projectile body is gravitation. When anything is thrown horizontally above, gravity is attracted to the ground vertically. The nature of the path of the motion trajectory is in a parabolic shape.
The projectile motion of any particle consists of two components as it is a 2D motion. They are horizontal x-component and vertical y-component.
The formula used to measure projectile motion is as follows,
v_{fx} = v_{ix} + a_{x}t
v_{fx}^{2} = v_{ix}^{2} + 2a_{x}x
Now it’s time to know the detailed approach of horizontal velocity.
The horizontal velocity of a projectile: Insights and Approach
In general, the motion of a projectile takes place when the object possesses sufficient velocity and has a path to travel.
Initially, when any particle is made to move upwards, it travels first along a horizontal path; the velocity possessed by the particle in motion along this horizontal path is considered the horizontal velocity of a projectile. Can measure it by taking the change in position or displacement of the projectile along horizontal with the time taken to complete that motion.
The horizontal motion of any projectile takes place as a result obtained by the particle’s motion to stay in the path of motion at a rate of constant velocity.
The value of the horizontal velocity of a projectile can be calculated using the below formulas,
v_{fx}^{2} = v_{ix}^{2} + 2a_{x}x
v_{fx} = v_{ix} + a_{x}t
v_{x} = Cos Θ
Now let us see the detail of how to find the horizontal velocity of a projectile with the help of a formula.
Approaches on how to find the horizontal velocity of a projectile
The formula to measure the motion of a projectile is given below,
Using this equation and from the kinematics, we can consider the equation to calculate the horizontal velocity. Can convert the equations mentioned above into horizontal motion by taking only the components of the x-axis that are considered horizontal components of any motion of the projectile. Later, we can interchange the terms in the equation to measure the required horizontal velocity.
- x = v_{ix}t + 1/2a_{x}t^{2}
- v_{fx} = v_{ix} + a_{x}t
- v_{fx}^{2} = v_{ix}^{2} + 2a_{x}x
In the above equations,
x refers to the horizontal change in position
a_{x} refers to the horizontal component of change in acceleration
v_{fx} refers to the final horizontal velocity
v_{ix} refers to initial horizontal velocity
t refers to the time taken to cover the path.
Theta refers to the angle of trajectory of the path
The formulas mentioned above are generally used to know how to find the horizontal velocity of a projectile.
Problems based on how to find the horizontal velocity of a projectile
Below are some problems on how to find the horizontal velocity of a projectile.
Problem 1
A ball made of rubber is thrown upwards with an initial velocity of 40m/s, and initially, the ball is made to launch at an angle of 25°. Find out the total horizontal velocity of the ball?
Solution: We have first to consider the given values.
Initial velocity = V_{i} = 40m/s
Θ = 25°
Now use the formula to find horizontal velocity,
V_{x} = V_{i}CosΘ
V= (40) Cos(25°)
V = 36.24m/s
Problem 2
A stone is thrown above with an initial velocity of 23m/s and is launched at an angle of 5°. Find out the total horizontal velocity of the ball?
Solution: We have first to consider the given values.
Initial velocity = V_{i} = 23m/s
Θ = 5°
Now use the formula to find horizontal velocity,
V_{x} = V_{i}CosΘ
V_{x} = (23) Cos(5°)
V_{x} = 22.908 m/s
It’s time to know the examples of how to find the horizontal velocity of a projectile.
Examples of the horizontal velocity of a projectile
The things you throw above will come down due to the nature of gravity. Here the motion is two-dimension and is termed as a projectile. The horizontal path is the initial motion that is almost observed in routine life. Here are some examples of the horizontal velocity of a projectile.
- Activating a cannonball upwards
- Playing a golf game
- Game of Hammer throw
- Water falling from a PVC pipe
- Shotput
- Launching of missiles
Activating a cannonball upwards
We have, in general, seen the launching of cannonballs in any clips or anime. As soon as the firearm of the system is lit, a canon moves upwards in a horizontal motion then moves down toward its required location. Here, the horizontal motion possesses horizontal velocity that can be measured using the formula mentioned above and is an example of finding the horizontal velocity of a projectile. Here the canon ball is the projectile.
Playing a golf game
A game of golf is one of the wealthiest international games as soon as the golf ball on the pitch is hit by the stick. It travels along a horizontal path above and reaches the required position. Here what happens is that the velocity possessed by the golf ball along the horizontal path is considered horizontal velocity. It can be measured using the formula to find the horizontal velocity.
Game of Hammer throw
The hammer throw game is considered one of the fittest games in the world. Even in this game, throwing a hammer takes place along the horizontal path; then, it takes a curve to reach the point of position. Here the hammer acts as a projectile, and its velocity along the horizontal path can be an example of how to find the horizontal velocity.
Water falling from a PVC pipe
In our daily routine, there will be flowing water from the pipe, and the flow takes place from high pressure to a low-pressure end when the motor starts to work after filling of tank, excess waterfalls. Here we must observe that initially, the flow will be horizontal, then the vertical motion takes place constructing a parabolic path. The horizontal flow of water will have constant horizontal velocity. We can use the above equations to find the value of its velocity.
Shotput
Even the game of shotput is somewhat similar to javelin and hammer throw. Here the shotput will act as a projectile. As soon as the player throws a shotput ball above, it travels along a horizontal path and reaches its destination. At this point, we can measure the horizontal distance and time to obtain the horizontal velocity of the shotput ball.
Launching of missiles
You must have seen the launching of missiles in any national channels. The path of this trajectory motion will be in the form of parabolic. Launching missiles requires more energy, and the velocity will be further higher than any other case of motion. Initially, these missiles travel along the horizontal path and then take a curve. We can find the angle and velocity using the formulas mentioned above.
These are some common examples of how to find the horizontal velocity of a projectile.
Vertical velocity of a projectile: Insights and Approach
The vertical velocity of a projectile is one more component of the projectile motion of the body, and it is contrary to horizontal motion.
Similarly, as we calculate the horizontal velocity of a projectile, we can take the component along the y-axis of the motion to find out the vertical velocity of a body in projectile motion. The velocity along the vertical direction does not depend on the horizontal direction.
Now let us know the formula using which we can measure the vertical velocity of the projectile.
How to find the final vertical velocity of a projectile?
The formula used to find the velocity along the vertical component of the projectile is given as follows,
v_{fy} = v_{iy} + a_{y}t
v_{ix2} = v_{iy2} + 2a_{y}y
V_{y} = Sin Θ_{y}
So, these are some approaches, examples, and problems based on how to find the horizontal velocity of a projectile.
To know more about Horizontal displacement
Frequently Asked Questions | FAQs
What do you mean by projectile motion?
The motion of a projectile is one of the crucial two-dimensional motions.
In physical science, projectile motion can be considered the motion influenced by only gravitational power. The nature of projectile motion is a parabolic curve. The specialty of this motion is it measures both horizontal and vertical components.
What is the definition of the horizontal velocity of a projectile?
The horizontal velocity is the velocity of any projectile along a horizontal path.
If any object is thrown into the air at any angle other than 90°, that particle or object moves in the trajectory path, making the curve’s nature parabolic.