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Initial Speed using Time of Flight Formula

GoInitial Speed given Maximum Height Formula

GoInitial Velocity using Range Formula

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Initial Velocity is the velocity of an object at the start of a motion, describing the object's initial state of motion. Check FAQs

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

u - Initial Velocity?T - Time of Flight?g - Acceleration due to Gravity?θ_pr - Angle of Projection?

Initial Speed using Time of Flight Example

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Here is how the Initial Speed using Time of Flight equation looks like with Values.

Here is how the Initial Speed using Time of Flight equation looks like with Units.

Here is how the Initial Speed using Time of Flight equation looks like.

35 = \frac{2.7816 \cdot 9.8}{2 \cdot \sin (0.4)}

35m/s = \frac{2.7816s \cdot 9.8m/s²}{2 \cdot \sin (0.4rad)}

35 = \frac{2.7816 \cdot 9.8}{2 \cdot \sin (0.4)}

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Initial Speed using Time of Flight Solution

Follow our step by step solution on how to calculate Initial Speed using Time of Flight?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

u = \frac{2.7816s \cdot 9.8m/s²}{2 \cdot \sin (0.4rad)}

Next Step Prepare to Evaluate

∴

u = \frac{2.7816 \cdot 9.8}{2 \cdot \sin (0.4)}

Next Step Evaluate

∴

u = 35.0000051851621m/s

LAST Step Rounding Answer

∴

u = 35m/s

Initial Speed using Time of Flight Formula Elements

Variables

Functions

Initial Velocity

Initial Velocity is the velocity of an object at the start of a motion, describing the object's initial state of motion.

Symbol: u

Measurement: SpeedUnit: m/s

Note: Value should be greater than 0.

Formulas to find Initial Velocity

Time of Flight

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.

Symbol: T

Measurement: TimeUnit: s

Note: Value can be positive or negative.

Formulas to find Time of Flight

Acceleration due to Gravity

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.

Symbol: g

Measurement: AccelerationUnit: m/s²

Note: Value should be greater than 0.

Formulas to find Acceleration due to Gravity

Angle of Projection

Angle of Projection is the angle at which an object is projected from the ground, influencing its trajectory and range of motion.

Symbol: θ_pr

Measurement: AngleUnit: rad

Note: Value can be positive or negative.

Formulas to find Angle of Projection

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.

Syntax: sin(Angle)

Other Formulas to find Initial Velocity

Go Initial Speed given Maximum Height

u = \frac{\sqrt{H max \cdot 2 \cdot g}}{\sin (θ pr)}

Go Initial Velocity using Range

u = \sqrt{g \cdot \frac{R motion}{\sin (2 \cdot θ pr)}}

Other formulas in Projectile Motion category

Go Maximum Height Attained for Inclined Projectile

H max = \frac{{(u \cdot \sin (θ inclination))}^{2}}{2 \cdot g \cdot \cos (α pl)}

Go Time of Flight for Inclined Projectile

T = \frac{2 \cdot u \cdot \sin (θ inclination)}{g \cdot \cos (α pl)}

Go Maximum Range of Flight for Inclined Projectile

R motion = \frac{u^{2} \cdot (1 - \sin (α pl))}{g \cdot {(\cos (α pl))}^{2}}

Go Maximum Height Attained by Object

v max = \frac{{(u \cdot \sin (θ pr))}^{2}}{2 \cdot g}

How to Evaluate Initial Speed using Time of Flight?

Initial Speed using Time of Flight evaluator uses Initial Velocity = (Time of Flight*Acceleration due to Gravity)/(2*sin(Angle of Projection)) to evaluate 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 evaluate Initial Speed using Time of Flight using this online evaluator? To use this online evaluator 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.

FAQs on Initial Speed using Time of Flight

What is the formula to find Initial Speed using Time of Flight?

The formula of Initial Speed using Time of Flight is expressed as Initial Velocity = (Time of Flight*Acceleration due to Gravity)/(2*sin(Angle of Projection)). Here is an example- 34.98038 = (2.78156*9.8)/(2*sin(0.4)).

How to calculate Initial Speed using Time of Flight?

With Time of Flight (T), Acceleration due to Gravity (g) & Angle of Projection (θ_pr) we can find Initial Speed using Time of Flight using the formula - Initial Velocity = (Time of Flight*Acceleration due to Gravity)/(2*sin(Angle of Projection)). This formula also uses Sine (sin) function(s).

What are the other ways to Calculate Initial Velocity?

Here are the different ways to Calculate Initial Velocity-

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))

Can the Initial Speed using Time of Flight be negative?

No, the Initial Speed using Time of Flight, measured in Speed cannot be negative.

Which unit is used to measure Initial Speed using Time of Flight?

Initial Speed using Time of Flight is usually measured using the Meter per Second[m/s] for Speed. Meter per Minute[m/s], Meter per Hour[m/s], Kilometer per Hour[m/s] are the few other units in which Initial Speed using Time of Flight can be measured.

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