In general, vertical velocity is used to launch the projectile. Vertical velocity is a topic of Physics. It is widely used for the projection of things. A projectile is a motion used for the constant acceleration to produce 2-D motion.

The projectile motion is a motion that makes the parabola while throwing from initial velocity and reaching the final position. In this post, we will go through the projectile motion for vertical velocity and how to calculate it with a lot of examples.

Table of Contents

## What is the projectile motion for vertical velocity?

In physics, a motion of an object thrown upward or projected into space is known as the projectile motion. When we throw the abject it goes away due to the force after some time the force of gravity is applied on that object and it comes down.

The object that we throw is said to be the projectile and the direction or distance of the object from initial to the final position is known as its trajectory. In other words, we can say that when the object is launched, it goes upward in the air just due to the vertical component of the initial velocity, from where the object is thrown.

It is mostly making a path like a parabola. There are many examples of projectile motion such that playing basketball in which a ball is thrown into the basket from some distance. And playing football in which when the ball is kicked with a great force it travels some distance and make a path like a parabola.

There is a formula for finding the velocity of the projectile motion of the vertical velocity.

V_{y} = v_{o} – g * t

In the above formula vo is the initial velocity form where the object is launched, g is the force of the gravity, and t is the time taken for reaching from initial to the final position.

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## Components of the velocity for projectile motion

There are two components of the velocity that are involved in the projectile motion for launching that is either horizontally or vertically.

### Horizontal Components

In the horizontal components of the velocity, an object continues its motion with a constant velocity. In simple words, a projectile continues its motion with a constant horizontal velocity just due to the absence of horizontal forces.

The range of the object or the projectile is the horizontal displacement of the projectile and it is dependent on the initial velocity form where the abject is launched. The range of the projectile must be the same if an object is projected at the constant starting speed with the two opposite angles.

To determine the distance of the horizontal components of the velocity for projectile motion can be written as.

Y = V x t

In the above equation, * v* is the constant velocity and

*is the time taken by the motion.*

**t**### Vertical Components

The vertical components of the projectile motion are handled by the force of gravity. In simple words, when an object is thrown upward there must be an unbalanced force that acts on the object and it will accelerate downward. This acceleration experiences the force of gravity and must be equal to 9.8m/sec^{2}.

To determine the distance of the vertical components of the velocity for projectile motion can be written as.

Y = h + V_{y} x t – g x t^{2} / 2

In the above equation, * h* is the height of the object from where the object is thrown,

**is the time, and**

*t***is the gravitational acceleration.**

*g*The calculation for throwing the objects away can easily be done with the help of the formula. Scientists make experiments by taking the calculation and throwing the object either it reaches or not to the required destination or not just with the help of the formula.

## How to calculate the projectile motion?

To calculate the projectile motion, we must have gravitational acceleration, initial velocity, and time. And if the projectile motion is given, we can calculate any term from gravitational acceleration, initial velocity, and time.

An online vertical velocity calculator can be used to find the projectile motion, gravitational acceleration, initial velocity, and time.

**Example 1**

A basketball player throws a ball from some distance making the projectile motion. The ball hit the ground after 13 seconds. What is the projectile motion for the vertical velocity if the initial velocity is 20 meters per second(m/s)?

*Solution*

Step 1: Determine the given information.

Time = 13 seconds

Initial velocity = v_{o} = 20 m/s

Acceleration of the gravity = g = 9.8 m/s^{2}

Step 2: Now take the general formula for calculating the projectile motion.

V_{y} = v_{o} – g * t

Step 3: Put the given values in the above formula to calculate the vertical velocity of the projectile motion.

V_{y} = v_{o} – g * t

V_{y} = 20m/s – 9.8m/s^{2} * 13s

V_{y} = 20m/s – 127.4m/s

**V _{y }= – 107.4 m/s**

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**Example 2**

A basketball player throws a ball from some distance making the projectile motion. The ball hit the ground after 7 seconds. And the projectile motion for the vertical velocity is – 27 m/s. Then what is the initial velocity?

*Solution*

Step 1: Determine the given information.

Time = 7 seconds

Initial velocity = v_{o} =?

Acceleration of the gravity = g = 9.8 m/s^{2}

Vertical velocity = V_{y} = – 27 m/s

Step 2: Now take the general formula for calculating the projectile motion.

V_{y} = v_{o} – g * t

Step 3: Rearrange the above formula.

v_{o} = V_{y} + g * t

Step 4: Put the given values in the above formula to calculate the initial velocity of the projectile motion.

v_{o} = V_{y} + g * t

v_{o} = – 27 m/s + 9.8m/s2 * 7s

v_{o} = – 27 m/s + 68.6 m/s

**v _{o} = 41.6 m/s**

## Conclusion

In this article, we have seen the equations of projectile motion for vertical velocity and components of projectile motion. Projectile motion for the vertical velocity is very essential for a different purpose in science and daily life. The most common use for the projectile motion is to throw the bomb or an object from one place to another by taking the exact calculations.