# Trajectory Calculator - Projectile Motion

Online Trajectory Projectile Motion Calculator Tool is provided here to get the trajectory of a projectile within no time. Just give velocity, angle of launch and initial height values in the allotted input sections and click on the calculate button to find the accurate output easily.

### Step by Step Process to Find Trajectory of Projectile Motion

The best and easiest way to compute the trajectory of an object are given below. Check out the instructions and follow them.

- Get the initial height, angle of launch, and initial velocity from the question.
- Find the tan function of angle and cos function of angle.
- Substitute the values in the formula.
- Perform the required math operations to check the trajectory.

### What is Meant by Trajectory?

The trajectory is the curved path of an object in relation with motion along with the gravity. It can also be called as projectile motion. In simple words, it is the curved path of an object under the gravity. The example of trajectory will br a ball thrown uwards, the path taken by the ball is determined by the gravity and resistance of air.

The trajectory formula is mentioned-below:

Vertical position = (horizontal osition) (tangent of launch angle) - [(acceleration due to gravity) (horizontal position)²] / [2(initial velocity)² (cosine of launch angle)²]

y = h + x * tan(α) - (g * x²)/(2 * V²_{o} * cos²(α))

Where,

g is the acceleration due to gravity

α is the angle of launch

h is the initial height

V_{o} is the initial velocity

**Example**

**Question: Suppose a water skier plans to set up a stunt in which he is going to jump over a burning obstacle. He jumps from a height of 4 m. The ramp is inclined at an angle of 40° in relation to the water. Furthermore, he plans to take off from the ramp at a velocity of 9.0 m/s. So, calculate if he will be able to jump over the flames or not?**

**Solution:**

Given that

Initial velocity V_{o} = 9 m/s

Height h = 4 m

Angle of launch α = 40°

The trajectory foermula is

y = h + x * tan(α) - (g * x²)/(2 * V²_{o} * cos²(α))

Substitute the given values

y = 4 + x * tan(40°) - (9.8 * x²)/(2 * 9² * cos²(40°))

y = 4 + x * 0.839 - 9.8x²/(2 * 81 * 0.586

= 4 + 0.839x - 9.8x²/95.05

Threrefore, trajectory formula is y = 4 + 0.839x - 9.8x²/95.05

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### Frequently Asked Questions on Trajectory Calculator

**1. How to calculate the equation of a trajectory in a projectile?**

The simple formula to calculate the equation of a projectile motion trajectory is y = h + x * tan(α) - (g * x²)/(2 * V²_{o} * cos²(α)). Substitute thre values and perform the operations to get the equation.

**2. What are the two components of projectile motion?**

The two components of the projectile motion are horizontal and vertical motion.

**3. What is the use of equation of trajectory in projectile motion?**

The trajectory projectile motion equation is used to find the distance of the curved path in the projectile.

**4. What is the shape of the trajectory of a projectile?**

A trajectory is the path taken by an moving object that is following as a function of time. The shape of trajectory is a curve.