Initial Speed using Time of Flight Calculator

✖Time of Flight is the duration of time an object is in the air after being projected from a source, such as a catapult or a hand.ⓘ Time of Flight [T]			+10% -10%
✖Acceleration due to Gravity is the rate of change of velocity of an object under the influence of gravitational force, typically measured in meters per second squared.ⓘ Acceleration due to Gravity [g]			+10% -10%
✖Angle of Projection is the angle at which an object is projected from the ground, influencing its trajectory and range of motion.ⓘ Angle of Projection [θ_pr]			+10% -10%

✖Initial Velocity is the velocity of an object at the start of a motion, describing the object's initial state of motion.ⓘ Initial Speed using Time of Flight [u]

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Formula

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Initial Speed using Time of Flight

Formula

u = \frac{T \cdot g}{2 \cdot \sin (θ pr)}

Example

35.00001 m/s = \frac{2.78156 s \cdot 9.8 m/s²}{2 \cdot \sin (0.4 rad)}

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Initial Speed using Time of Flight Solution

STEP 0: Pre-Calculation Summary

Formula Used

Initial Velocity = (Time of Flight*Acceleration due to Gravity)/(2*sin(Angle of Projection))
u = (T*g)/(2*sin(θ_pr))
This formula uses 1 Functions, 4 Variables

Functions Used

sin - Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse., sin(Angle)

Variables Used

Initial Velocity - (Measured in Meter per Second) - Initial Velocity is the velocity of an object at the start of a motion, describing the object's initial state of motion.
Time of Flight - (Measured in Second) - Time of Flight is the duration of time an object is in the air after being projected from a source, such as a catapult or a hand.
Acceleration due to Gravity - (Measured in Meter per Square Second) - Acceleration due to Gravity is the rate of change of velocity of an object under the influence of gravitational force, typically measured in meters per second squared.
Angle of Projection - (Measured in Radian) - Angle of Projection is the angle at which an object is projected from the ground, influencing its trajectory and range of motion.

STEP 1: Convert Input(s) to Base Unit

Time of Flight: 2.78156 Second --> 2.78156 Second No Conversion Required
Acceleration due to Gravity: 9.8 Meter per Square Second --> 9.8 Meter per Square Second No Conversion Required
Angle of Projection: 0.4 Radian --> 0.4 Radian No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

u = (T*g)/(2*sin(θ_pr)) --> (2.78156*9.8)/(2*sin(0.4))

Evaluating ... ...

u = 35.0000051851621

STEP 3: Convert Result to Output's Unit

35.0000051851621 Meter per Second --> No Conversion Required

FINAL ANSWER

35.0000051851621 ≈ 35.00001 Meter per Second <-- Initial Velocity

(Calculation completed in 00.004 seconds)

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Created by Mayank Tayal

National Institute of Technology (NIT), Durgapur

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National Institute Of Technology (NIT), Hamirpur

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< Projectile Motion Calculators

Maximum Height Attained for Inclined Projectile

Go Maximum Height = ((Initial Velocity*sin(Angle of Inclination))^2)/(2*Acceleration due to Gravity*cos(Angle of Plane))

Maximum Range of Flight for Inclined Projectile

Go Range of Motion = (Initial Velocity^2*(1-sin(Angle of Plane)))/(Acceleration due to Gravity*(cos(Angle of Plane))^2)

Time of Flight for Inclined Projectile

Go Time of Flight = (2*Initial Velocity*sin(Angle of Inclination))/(Acceleration due to Gravity*cos(Angle of Plane))

Maximum Height Attained by Object

Go Maximum Height of Crack = ((Initial Velocity*sin(Angle of Projection))^2)/(2*Acceleration due to Gravity)

Initial Speed using Time of Flight Formula

Initial Velocity = (Time of Flight*Acceleration due to Gravity)/(2*sin(Angle of Projection))
u = (T*g)/(2*sin(θ_pr))

What is Projectile Motion ?

Projectile motion is a type of two-dimensional motion or motion in a plane. It is assumed that the only force acting on a projectile (the object experiencing projectile motion) is the force due to gravity.

How to Calculate Initial Speed using Time of Flight?

Initial Speed using Time of Flight calculator uses Initial Velocity = (Time of Flight*Acceleration due to Gravity)/(2*sin(Angle of Projection)) to calculate the Initial Velocity, Initial Speed using Time of Flight formula is defined as a measure of the initial velocity of an object under the sole influence of gravity, considering the time of flight and the angle of projection, providing valuable insights into the kinematics of motion. Initial Velocity is denoted by u symbol.

How to calculate Initial Speed using Time of Flight using this online calculator? To use this online calculator for Initial Speed using Time of Flight, enter Time of Flight (T), Acceleration due to Gravity (g) & Angle of Projection (θ_pr) and hit the calculate button. Here is how the Initial Speed using Time of Flight calculation can be explained with given input values -> 34.98038 = (2.78156*9.8)/(2*sin(0.4)).

FAQ

What is Initial Speed using Time of Flight?

Initial Speed using Time of Flight formula is defined as a measure of the initial velocity of an object under the sole influence of gravity, considering the time of flight and the angle of projection, providing valuable insights into the kinematics of motion and is represented as u = (T*g)/(2*sin(θ_pr)) or Initial Velocity = (Time of Flight*Acceleration due to Gravity)/(2*sin(Angle of Projection)). Time of Flight is the duration of time an object is in the air after being projected from a source, such as a catapult or a hand, Acceleration due to Gravity is the rate of change of velocity of an object under the influence of gravitational force, typically measured in meters per second squared & Angle of Projection is the angle at which an object is projected from the ground, influencing its trajectory and range of motion.

How to calculate Initial Speed using Time of Flight?

Initial Speed using Time of Flight formula is defined as a measure of the initial velocity of an object under the sole influence of gravity, considering the time of flight and the angle of projection, providing valuable insights into the kinematics of motion is calculated using Initial Velocity = (Time of Flight*Acceleration due to Gravity)/(2*sin(Angle of Projection)). To calculate Initial Speed using Time of Flight, you need Time of Flight (T), Acceleration due to Gravity (g) & Angle of Projection (θ_pr). With our tool, you need to enter the respective value for Time of Flight, Acceleration due to Gravity & Angle of Projection and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Initial Velocity?

In this formula, Initial Velocity uses Time of Flight, Acceleration due to Gravity & Angle of Projection. We can use 2 other way(s) to calculate the same, which is/are as follows -

Initial Velocity = (sqrt(Maximum Height*2*Acceleration due to Gravity))/sin(Angle of Projection)
Initial Velocity = sqrt(Acceleration due to Gravity*Range of Motion/sin(2*Angle of Projection))

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