Created By : Vaibhavi Kumari

Reviewed By : Rajashekhar Valipishetty

Last Updated : May 07, 2023

The trajectory calculator developed by us gives an accurate answer in regard to any question related to the projectile motion’s path in the space. A trajectory calculator is generally used to find the range, maximum height, and flight time of horizontal projectiles.

Angle of launch:
Initial height:

Trajectory Definition

Trajectory also called a flight path in the projectile motion, is the path followed by a moving object under the action of gravity without any external force acting upon it. Usually, the term is used when we talk about projectiles or satellites in space is the trajectory rather than the projectile. If an object is thrown for short distances as on earth frame of reference, then a parabola is a good approximation of trajectory shape to solve questions.

Projectile Motion Trajectory Formulas

From the equations of laws of the motion, we have: x = Vx * t, y = h + Vy * t - g * t² / 2

Subsequently, we know that three vectors - V₀, Vx and Vy - form a right triangle, where all the values take one magnitude in respective x,y, and z-direction, so we can write that the horizontal velocity component Vx is equal to V₀ * cos(α).

Considering alpha to be the value of angle made by the object and the ground. The vertical velocity component Vy = V₀ * sin(α) Then, we combine the equations of motion and velocity components into one formula and hence we get

  • y = h + Vy * t - g * t² / 2 = h + x * Vy / Vx - g * (x / Vx)² / 2
  • y = h + x * (V₀ * sin(α)) / (V₀ * cos(α)) - g * (x / V₀ * cos(α))² / 2

How to find Trajectory of Projectile Motion?

Follow the simple and easy steps listed below to determine the trajectory of projectile motion. They are along the lines

  • First and foremost step is to determine the values of initial height, angle of launch, and initial velocity.
  • And then determine the tan and cos function of angle.
  • Now, substitute the values obtained in the formula of trajectory of projectile motion.
  • Do the required math calculations and obtain the trajectory.

How does the Trajectory Projectile Motion Calculator work?

  • Enter the values of Alpha that is the value of the angle between the ground and the projectile and ‘g’ is the gravitational acceleration under free fall and ‘v’ that is the velocity of the object thrown.
  • Then the calculator works on the formula of trajectory formula that is y = h + x * (V₀ * sin(α)) / (V₀ * cos(α)) - g * (x / V₀ * cos(α))² / 2 and computes the answer.
  • The results section shows you the estimated elapsed time over the projectile once you enter all the values and proceed.

Trajectory of a Projectile Examples

Question 1: Jack throws a ball at an angle of 60 degrees in the air. If it moves at the rate of 6m/s and John catches it after 4s. Calculate the vertical distance covered by the ball in the meantime.


Given that the angle of the ball with the ground is 60 degrees.

The initial velocity of the ball is hence 6m/sec

Time is taken by the ball in the air = 4 sec

The horizontal distance is given by:


x = 24 m

Subsituting it in the formula y = h + x * (V₀ * sin(α)) / (V₀ * cos(α)) - g * (x / V₀ * cos(α))² / 2 we get,

y = (24)(1.7320) – [ (9.8)(24)(24)/(2)(36)(0.25)]

y =41.568 – [5644.8/18]

y=41.568 – 313.6

y= – 272.032 m

Question 2: If the initial velocity of a stone thrown by a boy is 6 m/sec, and the angle at which the stone is thrown is 60∘. Find the equation of the path of the projectile. Use g = 9.8 m/sec2. Solve this by using the trajectory formula?


Given, that the angle of the stone is θ = 60∘.

v(initial velocity) of the stone = 6m /sec

Using the trajectory formula,


Subsitutuing the values,

y = x tan 60 - (9.8)(x2)/(2)(62)(cos2 60)

y = x√3 - 0.544x2

FAQs on Trajectory of a Projectile Motion

1. How do you calculate time in projectile motion?

To calculate the time of flight of equation, we should split the formulas into two cases: (initial height = 0) and hence t = 2 * V₀ * sin(α) / g and (initial height > 0) then t = [V₀ * sin(α) + √((V₀ * sin(α))² + 2 * g * h)] / g.

2. What is the range of projectile motion?

The horizontal distance of the projectile covered in a particular time is called the range of the projectile.

3. What is projectile motion?

Any object that we throw in the air and cover a path of trajectory is said to be in projectile motion.

4. How do you calculate the range of a projectile?

By the formula of d = V₀² * sin(2 * α) / g, where v stands for velocity, alpha for the angle at which the projectile has been thrown, and g for the gravity of the place in which the experiment is being done.

5. What is vertical velocity?

Velocity in the vertical motion of the object or in the upward/downward motion of an object.