Time of Flight Calculator

What is the Time of Flight?

The time of flight is the time taken to travel at a specific trajectory through the air. Launch angle and initial velocity determine the time of flight of an object.

You need to measure the distance, initial speed, and the launching angle to find the location of the object. Finding the initial projectile angle and velocity makes it possible to pinpoint an object at a particular moment. Initial angle and velocity respectively can be calculated by the air calculator. It can be quite interesting to know the height and how to find how long something is in the air. 

Time of Flight Formula:

The formula for the time of flight depends on the initial velocity and the angle of projection. The time of flight equation is given by:

\[ t = \frac{V_0 \sin(\alpha) + \sqrt{(V_0 \sin(\alpha))^2 + 2 g h}}{g} \]

Where:

• V₀ = Initial velocity
• α = Angle of projection
• g = Acceleration due to gravity
• h = Initial height from which the projectile is launched

Projectile motion and time of flight are crucial for applications such as missile tests, where the location of the projectile must be known at a specific time. Our efficient ballistic time of flight calculator is specifically designed to calculate the projectile motion of a missile.

Example:

Let's suppose the angle of projection of an object is 45 degrees, the initial height and velocity of the object are 5 m and 30 m/sec respectively. The gravitational pull is 9.80665 m/sec^2, then find how long an object is in the air.

Given:

V_o = 30 m/sec

α = 45 degrees

h = 5m

g = 9.80665 m/sec^2

Solution:

\( t = \dfrac{V_o sin(α) + \sqrt{(V_o sin(α))^2 + 2gh}}{g}\)

Enter the values in the time flight equation, for simplification use the time of flight calculator.

\(t = \dfrac{30 \times sin(45) + \sqrt{(30 \times sin(45))^2 + 2 \times9.807\times5}}{9.807}\)

\( t = \dfrac{30 \times 0.7071 + \sqrt{(30 \times 0.7071)^2 + 2 \times9.807\times5}}{9.807}\) 

\(t = \dfrac{21.21 + \sqrt{548.0665}}{9.807}\) 

\( t = \dfrac{44.62}{9.807}\) 

\( \text{t = 4.55 sec}\) 

The time of flight of the object is 4.55 sec when checked by the projectile motion time calculator

Working of Time of Flight Calculator:

Operating our hang time calculator is quite as it requires the following input values to generate accurate results. 

Input:

• Enter the angle of launch, initial velocity, and height of the object 
• Hit the Calculate Button

Output:

• Time of flight

References:

From the source of Openstax.org: Time of Flight, Projectile Motion Time of Flight From the source of Wikipedia.org: Projection Angle, Time of Flight Formula