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Initial Velocity of Particle given Time of Flight of Projectile Formula

GoInitial Velocity of Particle given Horizontal Component of Velocity Formula

GoInitial Velocity of Particle given Vertical Component of Velocity Formula

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Initial Velocity of Projectile Motion is the velocity at which motion starts. Check FAQs

v pm = \frac{[g] \cdot t pr}{2 \cdot \sin (α pr)}

v_pm - Initial Velocity of Projectile Motion?t_pr - Time Interval?α_pr - Angle of Projection?[g] - Gravitational acceleration on Earth?

Initial Velocity of Particle given Time of Flight of Projectile Example

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Here is how the Initial Velocity of Particle given Time of Flight of Projectile equation looks like with Values.

Here is how the Initial Velocity of Particle given Time of Flight of Projectile equation looks like with Units.

Here is how the Initial Velocity of Particle given Time of Flight of Projectile equation looks like.

29.4761 = \frac{9.8066 \cdot 4.25}{2 \cdot \sin (44.99)}

29.4761m/s = \frac{9.8066m/s² \cdot 4.25s}{2 \cdot \sin (44.99°)}

29.4761 = \frac{9.8066 \cdot 4.25}{2 \cdot \sin (44.99)}

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Initial Velocity of Particle given Time of Flight of Projectile Solution

Follow our step by step solution on how to calculate Initial Velocity of Particle given Time of Flight of Projectile?

FIRST Step Consider the formula

v pm = \frac{[g] \cdot t pr}{2 \cdot \sin (α pr)}

Next Step Substitute values of Variables

∴

v pm = \frac{[g] \cdot 4.25s}{2 \cdot \sin (44.99°)}

Next Step Substitute values of Constants

∴

v pm = \frac{9.8066m/s² \cdot 4.25s}{2 \cdot \sin (44.99°)}

Next Step Convert Units

∴

v pm = \frac{9.8066m/s² \cdot 4.25s}{2 \cdot \sin (0.7852rad)}

Next Step Prepare to Evaluate

∴

v pm = \frac{9.8066 \cdot 4.25}{2 \cdot \sin (0.7852)}

Next Step Evaluate

∴

v pm = 29.4761270454251m/s

LAST Step Rounding Answer

∴

v pm = 29.4761m/s

Initial Velocity of Particle given Time of Flight of Projectile Formula Elements

Variables

Constants

Functions

Initial Velocity of Projectile Motion

Initial Velocity of Projectile Motion is the velocity at which motion starts.

Symbol: v_pm

Measurement: SpeedUnit: m/s

Note: Value should be greater than 0.

Formulas to find Initial Velocity of Projectile Motion

Time Interval

Time interval is what a clock reads, it is a scalar quantity.

Symbol: t_pr

Measurement: TimeUnit: s

Note: Value should be greater than 0.

Formulas to find Time Interval

Angle of Projection

Angle of Projection is angle made by the particle with horizontal when projected upwards with some initial velocity.

Symbol: α_pr

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Angle of Projection

Gravitational acceleration on Earth

Gravitational acceleration on Earth means that the velocity of an object in free fall will increase by 9.8 m/s2 every second.

Symbol: [g]

Value: 9.80665 m/s²

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 of Projectile Motion

Go Initial Velocity of Particle given Horizontal Component of Velocity

v pm = \frac{v h}{\cos (α pr)}

Go Initial Velocity of Particle given Vertical Component of Velocity

v pm = \frac{v v}{\sin (α pr)}

Go Initial Velocity given Maximum Horizontal Range of Projectile

v pm = \sqrt{H max \cdot [g]}

Other formulas in Projectile Motion category

Go Horizontal Component of Velocity of Particle Projected Upwards from Point at Angle

v h = v pm \cdot \cos (α pr)

Go Vertical Component of Velocity of Particle Projected Upwards from Point at Angle

v v = v pm \cdot \sin (α pr)

Go Time of Flight of Projectile on Horizontal Plane

t pr = \frac{2 \cdot v pm \cdot \sin (α pr)}{[g]}

Go Horizontal Range of Projectile

H = \frac{{v pm}^{2} \cdot \sin (2 \cdot α pr)}{[g]}

How to Evaluate Initial Velocity of Particle given Time of Flight of Projectile?

Initial Velocity of Particle given Time of Flight of Projectile evaluator uses Initial Velocity of Projectile Motion = ([g]*Time Interval)/(2*sin(Angle of Projection)) to evaluate the Initial Velocity of Projectile Motion, Initial Velocity of Particle given Time of Flight of Projectile formula is defined as the velocity at which a particle is projected from the ground, calculated by considering the time of flight, acceleration due to gravity, and the angle of projection, providing a crucial parameter in understanding projectile motion. Initial Velocity of Projectile Motion is denoted by v_pm symbol.

How to evaluate Initial Velocity of Particle given Time of Flight of Projectile using this online evaluator? To use this online evaluator for Initial Velocity of Particle given Time of Flight of Projectile, enter Time Interval (t_pr) & Angle of Projection (α_pr) and hit the calculate button.

FAQs on Initial Velocity of Particle given Time of Flight of Projectile

What is the formula to find Initial Velocity of Particle given Time of Flight of Projectile?

The formula of Initial Velocity of Particle given Time of Flight of Projectile is expressed as Initial Velocity of Projectile Motion = ([g]*Time Interval)/(2*sin(Angle of Projection)). Here is an example- 29.47098 = ([g]*4.25)/(2*sin(0.785223630472101)).

How to calculate Initial Velocity of Particle given Time of Flight of Projectile?

With Time Interval (t_pr) & Angle of Projection (α_pr) we can find Initial Velocity of Particle given Time of Flight of Projectile using the formula - Initial Velocity of Projectile Motion = ([g]*Time Interval)/(2*sin(Angle of Projection)). This formula also uses Gravitational acceleration on Earth constant(s) and Sine function(s).

What are the other ways to Calculate Initial Velocity of Projectile Motion?

Here are the different ways to Calculate Initial Velocity of Projectile Motion-

Initial Velocity of Projectile Motion=Horizontal Component of Velocity/cos(Angle of Projection)
Initial Velocity of Projectile Motion=Vertical Component of Velocity/sin(Angle of Projection)
Initial Velocity of Projectile Motion=sqrt(Maximum Horizontal Range*[g])

Can the Initial Velocity of Particle given Time of Flight of Projectile be negative?

No, the Initial Velocity of Particle given Time of Flight of Projectile, measured in Speed cannot be negative.

Which unit is used to measure Initial Velocity of Particle given Time of Flight of Projectile?

Initial Velocity of Particle given Time of Flight of Projectile 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 Velocity of Particle given Time of Flight of Projectile can be measured.

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Initial Velocity of Particle given Time of Flight of Projectile Formula

​GoInitial Velocity of Particle given Horizontal Component of Velocity Formula

​GoInitial Velocity of Particle given Vertical Component of Velocity Formula

Initial Velocity of Particle given Time of Flight of Projectile Example

Initial Velocity of Particle given Time of Flight of Projectile Solution

Initial Velocity of Particle given Time of Flight of Projectile Formula Elements

Other Formulas to find Initial Velocity of Projectile Motion

Other formulas in Projectile Motion category

How to Evaluate Initial Velocity of Particle given Time of Flight of Projectile?

FAQs on Initial Velocity of Particle given Time of Flight of Projectile

Variable Name

GoInitial Velocity of Particle given Horizontal Component of Velocity Formula

GoInitial Velocity of Particle given Vertical Component of Velocity Formula