Parabolic Motion Material: Formulas and Example Problems

The parabolic motion formula is usually one of the formulas you are looking for. Basically, parabolic motion is also known as bullet motion. It is named parabolic motion because its trajectory has a parabolic shape, not moving in a straight line.

We can see examples of parabolic motion in everyday life, for example, such as the movement of objects thrown from an airplane to the motion of a cannonball being fired.

Definition of Parabolic Motion

Parabolic motion is a movement with a trajectory that is not straight but in the form of a parabola. This is due to the combination of GLB or Uniform Straight Motion and GLBB or Uniformly Changing Straight Motion.

These two motions eventually form an angle of elevation on the horizontal or X axis and the vertical or Y axis. The X axis is GLB while the Y axis is GLBB. So, both have a curved path called a parabolic motion.

The parabolic motion is initially driven by an initial velocity and then travels a trajectory in a direction influenced by gravity. The term bullet motion in parabolic motion is caused because the type of motion when the bullet is fired also has the same trajectory.

There are various characteristics of parabolic motion, namely:

1. Parabolic motion of an object due to an applied force. In the discussion of dynamics in physics, force is the cause of the motion of objects. In the discussion of parabolic motion, we focus more on the motion of objects after being thrown and moving freely in the air.
2. Like a free fall motion, an object that performs a parabolic motion is influenced by the force of gravity and has a downward direction or the center of the earth of g = 9.8 m/s2.
3. There are obstacles that make objects when fired, thrown or kicked with initial speed, movement depends on gravity and resistance.

Read: Power Formula

Characteristics of Parabolic Motion

The following are the various characteristics of parabolic motion, namely:

1. The farthest motion is taken using an angle of 45°
2. The pair of angles that produce an angle with the number 90° can later produce the same distance traveled
3. Mass has no influence on the angle of elevation as long as the initial velocity is constant

Read: Transformer Formula

Parabolic Motion Formula

How about the formula? There are several formulas for this parabolic motion. Here are some of them, such as:

1. The formula for motion of the parabola at the starting point

Basically, the shot bullet has an initial velocity. When forming a curved path there will be an angle formed. Therefore, later we will include the angle in the calculation of the initial velocity.

With this, we obtain the initial velocity equation for horizontal motion (V_0x) as well as vertical (V_0y), that is:

• Initial velocity in horizontal motion (V_0x)

V_0x = V cos

• Initial velocity in vertical motion (V_0y)

V_0y = V sin

• Initial speed (V)

V = V_0x+ V_0y

Information:

• V = initial velocity
• V_0x= initial speed x axis
• V_0y= initial velocity of the y-axis
• = angle made about the positive x axis

2. Parabolic Motion Formula at Point A

After understanding the explanation of the formula above, then the motion on the X axis is analyzed by GLB. Therefore, for a velocity equal to the velocity V_0x. While V_y will be pushed by gravity which pulls and unique objects downward so that the speed will decrease.

For horizontal distances, the GLB distance formula will be used, while the vertical or height distances will use the GLBB formula. With this equation, there is an equation, namely:

• x-axis speed

V_x = V_0x = V cos

• y-axis speed

V_y = V_0y – gt
V_y = V sin – gt

• Distance on the x-axis

X = V_0x. t

• Distance on the y-axis

Y = V_0y. t –

1 / 2

gt²

Information

• V = initial velocity
• V_0x= initial speed x axis
• V_x= x-axis speed
• V_0y= initial velocity of the y-axis
• V_y= speed on the y-axis
• g = gravity
• t = travel time
• = angle made about the positive x axis
• X = distance to the x-axis
• Y = distance to the y-axis

3. Parabolic Motion Formula at Point B

Point B is the highest point symbolized as h or y_max. In order for an object to reach its maximum height, the condition V_y = 0. So the velocity at the highest point is on the x-axis (V_x ). The following is an equation that can be formulated when it is at the maximum point B:

a. The highest point that can be reached
h =

V_0y² / 2g

h =

V² sin² / 2g

b. Time to reach the highest point (B)
V_y = 0
V_y = V_0y – gt
0 = V sin – gt
t =

(V x sin ) / g

t =

V_0y /g

c. Horizontal distance from starting point to point B
X = V_0x x t
X = V cos x

V sin / g

X =

V² x cos x sin / g

X =

V² x sin 2θ / g

Information

• V: initial speed
• V_0x:initial velocity on the x-axis
• V_x: x-axis speed
• V_0y: initial velocity on the y-axis
• V_y: y-axis speed
• g: gravity
• t: travel time unit time
• X: distance to x-axis
• h: maximum height

4. Parabolic Motion Formula for Point C

The motion at point C is actually the same and resembles the motion of the parabola at point A. However, the difference is in the gravitational motion which has a factual value. This is because it is heading downwards.

Because it is said to be the same and similar to through A, the motion on the X axis will still use GLB while Y will use GLBB but the gravity it has has a positive value. With this equation, there are several similarities, namely:

• Speed ​​on the x-axis

V_x = V_0x = V cos

• Speed ​​on y-axis

V_y = V_0y + gt
V_y = V sin + gt

5. Parabola Motion Formula At Point D

Point D is the farthest distance an object can travel in a parabolic motion. The farthest distance can be symbolized by X_max. This maximum distance can also be said as the distance an object returns to the ground after the object performs a parabolic motion.

The time it takes for an object to reach the ground is 2 times the time it takes the object to reach the distance when it is at its highest point. Here's the equation:

Speed ​​on the x-axis
V_x= V_0x = V. cos

Speed ​​on y-axis
V_y= V sin + gt

Time taken to reach the ground (point D)t = 2.

V_0y /g

t =

V. sin / g

Maximum distance (Distance from the start of the ball moving to point D)

X_max= V² sin 2θ / 2g

Information

• V: initial speed
• V_0x: initial velocity x axis
• V_x: x-axis speed
• V_0y: initial velocity of the y-axis
• V_y: y-axis speed
• g: gravity
• t: travel time
• X: distance to x-axis
• X_max: maximum distance

Read: Density Formula

Parabolic Motion Component

As in the parabolic motion material, this motion has components, namely:

1. Horizontal Side Motion Component

The horizontal motion component has a magnitude that is always fixed in each time span, this is because there is no acceleration and deceleration of the X axis.

In addition, there is also an angle between the object's velocity and the horizontal motion component in each time span. Finally, there is no acceleration or deceleration on the X-axis.

2. Components of Parabolic Motion on the Vertical Side

As for the vertical motion, it has a magnitude that always changes in each range, this is due to the influence of the acceleration due to gravity on the y-axis.

Example of Parabolic Motion Problem

To make the material about parabolic motion clearer, here is an example problem:

One of the bullets fell exactly 10 meters in front of Sandra and her elevation angle was 45 degrees. Determine the initial velocity of the bullet

Answer:

Andi kicks the ball with an initial speed of 15 m/s, and has an elevation angle of 45 degrees. Determine the maximum trajectory length of the ball

Answer:

The parabolic motion formula is indeed not as easy as imagined to memorize. However, with continuous practice, we will get used to doing it.