What is Parabolic Motion?

Parabolic motion is a combination of regular straight motion or (GLB) on the x-axis (horizontal) and regular-changing straight motion (GLBB) on the y-axis (vertical).

Parabolic Motion Components

Parabolic Motion

If you look at the picture above, it is identified with several components of the motion. There is a component of horizontal movement on the x-axis and vertical on the y-axis. The following is an explanation of each component.

  1. The x-axis component

What is contained in the x-axis component is a regular straight motion (GLB). That is, the velocity that an object has at any point or position on the horizontal axis is constant.


This is caused by no acceleration or deceleration on the x-axis. The x-axis components include initial velocity, evaluation angle, and initial velocity on the x-axis. The following form the equation that is on the x-axis


The x-axis equation




  1. The y-axis component

In contrast to the x-axis component which is a regular straight motion (GLB), the component on the y-axis is a straight change in order (GLBB).


This happens because on the y axis, an object is accelerating or decelerating. The y-axis components include initial velocity on the y-axis, evaluation angle, and initial velocity.


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We can also find the height of an object at certain intervals on the y-axis. For more details, consider the following equation.


The y-axis equation




Parabola Motion Formula

The x-axis for parabolic motion has been set for the following formulas:




X = Vοx = Vοcosθxt


After getting the velocity from the x-axis, which is (Vx) and the velocity from the y-axis, namely (Vy), we can find a value for the total velocity, namely (Vg), using the resultant velocity formula, which is as follows:


Vr = √Vx² + Vy ² maka, tanθ = Vy / Vx


Time when you reach the tipping point

The vertex of the motion of the parabola is when an object is at its maximum height about the y axis. In that state, the object’s velocity is 0 or mathematically written as V y  = 0.


The formula for determining the time when the object reaches its peak can be written as follows.


tp = (vosinθ)/g


In addition, you can also find out the time to reach the original height using the 2 x formula that was written above. Consider the following formula as a formula for determining when an object returns to its original position.


tT=2 xtp=2x(vosinθ)/g


Determining the Maximum Achievable Height

In the motion of a parabola, you can also calculate the maximum height on the y-axis that can be reached by an object using the following formula.


hmax = (vo2sin2θ)/2g


Determining the Maximum Achievable Distance

In addition, the motion of a parabola can also find out the maximum distance to the x-axis that can be reached by an object. The formula that can be used is as follows.


Information :


Vox = initial velocity of the axis.x (m / s)

Voy = initial velocity of the y axis (m / s) vx = velocity after a certain time (t) on the axis (m / s)

Vy = velocity after a certain time (t) on the y axis (m / s)

Vr = total velocity (m / s)

x = position of object on x axis (horizontal) (m)

y = the position of its object on the y-axis (vertical) (m)

t = time (s)

g = acceleration due to gravity (m / s)

θ = elevation angle (º)

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Example of Parabolic Motion Problems

A bullet is fired from the muzzle of a cannon with a speed of 50 m / s horizontally from the top of a hill, illustration as shown below.




acceleration due to gravity = 10 m / s2

hill height = 100 m


  1. The time it takes for bullets to reach the ground
  2. Horizontal distance reached by bullet (S)




  1. a) The time it takes for the bullet to reach the ground


When looking at the Y axis, which is a free motion. So that Voy = O and the height of the hill is called Y (in the problem it is called h)


Y = 1/2 g t2

100 = (1/2)(10) t2

t = √20 = 2√5 seconds

So, the  time it takes for the bullet to reach the ground is 2√5 seconds


  1. b) Horizontal distance achieved by bullet (S)


Namely in the form of GLB because the angle is zero to the horizontal and the formula:




Thus,   At the flat distance reached the bullet (S) is 100 √5 meters

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