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(θpr))
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 at which motion starts.
Time of Flight - (Measured in Second) - Time of Flight is defined as the time taken by the liquid particle in a liquid jet to reach from origin to maximum horizontal distance.
Acceleration due to Gravity - (Measured in Meter per Square Second) - Acceleration due to Gravity is acceleration gained by an object because of gravitational force.
Angle of Projection - (Measured in Radian) - Angle of Projection is angle made by the particle with horizontal when projected upwards with some initial velocity.
STEP 1: Convert Input(s) to Base Unit
Time of Flight: 4.5 Second --> 4.5 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(θpr)) --> (4.5*9.8)/(2*sin(0.4))
Evaluating ... ...
u = 56.6229106448286
STEP 3: Convert Result to Output's Unit
56.6229106448286 Meter per Second --> No Conversion Required
FINAL ANSWER
56.6229106448286 56.62291 Meter per Second <-- Initial Velocity
(Calculation completed in 00.020 seconds)

Credits

Created by Mayank Tayal
National Institute of Technology (NIT), Durgapur
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National Institute Of Technology (NIT), Hamirpur
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7 Projectile Motion ( object thrown at some angle 'theta' ) Calculators

Height of Object given Horizontal Distance
Go Height of Crack = Horizontal Distance*tan(Angle of Projection)-(Acceleration due to Gravity*Horizontal Distance^2)/(2*(Initial Velocity*cos(Angle of Projection))^2)
Initial Speed given Maximum Height
Go Initial Velocity = (sqrt(Maximum Height*2*Acceleration due to Gravity))/sin(Angle of Projection)
Initial Velocity using Range
Go Initial Velocity = sqrt(Acceleration due to Gravity*Range of Motion/sin(2*Angle of Projection))
Maximum Height Attained by Object
Go Height of Crack = ((Initial Velocity*sin(Angle of Projection))^2)/(2*Acceleration due to Gravity)
Range of Projectile Motion
Go Range of Motion = (Initial Velocity^2*sin(2*Angle of Projection))/Acceleration due to Gravity
Initial Speed using Time of Flight
Go Initial Velocity = (Time of Flight*Acceleration due to Gravity)/(2*sin(Angle of Projection))
Time of Flight
Go Time of Flight = (2*Initial Velocity*sin(Angle of Projection))/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(θpr))

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, The Initial Speed using Time of Flight formula is defined as the velocity of the object before acceleration causes a change. After accelerating for some amount of time, the new velocity is the final velocity. 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 pr) and hit the calculate button. Here is how the Initial Speed using Time of Flight calculation can be explained with given input values -> 56.62291 = (4.5*9.8)/(2*sin(0.4)).

FAQ

What is Initial Speed using Time of Flight?
The Initial Speed using Time of Flight formula is defined as the velocity of the object before acceleration causes a change. After accelerating for some amount of time, the new velocity is the final velocity and is represented as u = (T*g)/(2*sin(θpr)) or Initial Velocity = (Time of Flight*Acceleration due to Gravity)/(2*sin(Angle of Projection)). Time of Flight is defined as the time taken by the liquid particle in a liquid jet to reach from origin to maximum horizontal distance, Acceleration due to Gravity is acceleration gained by an object because of gravitational force & Angle of Projection is angle made by the particle with horizontal when projected upwards with some initial velocity.
How to calculate Initial Speed using Time of Flight?
The Initial Speed using Time of Flight formula is defined as the velocity of the object before acceleration causes a change. After accelerating for some amount of time, the new velocity is the final velocity 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 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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