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Initial Velocity given Maximum Horizontal Range 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 = \sqrt{H max \cdot [g]}

v_pm - Initial Velocity of Projectile Motion?H_max - Maximum Horizontal Range?[g] - Gravitational acceleration on Earth?

Initial Velocity given Maximum Horizontal Range of Projectile Example

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Here is how the Initial Velocity given Maximum Horizontal Range of Projectile equation looks like with Values.

Here is how the Initial Velocity given Maximum Horizontal Range of Projectile equation looks like with Units.

Here is how the Initial Velocity given Maximum Horizontal Range of Projectile equation looks like.

31.0008 = \sqrt{98 \cdot 9.8066}

31.0008m/s = \sqrt{98m \cdot 9.8066m/s²}

31.0008 = \sqrt{98 \cdot 9.8066}

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Initial Velocity given Maximum Horizontal Range of Projectile Solution

Follow our step by step solution on how to calculate Initial Velocity given Maximum Horizontal Range of Projectile?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

v pm = \sqrt{98m \cdot [g]}

Next Step Substitute values of Constants

∴

v pm = \sqrt{98m \cdot 9.8066m/s²}

Next Step Prepare to Evaluate

∴

v pm = \sqrt{98 \cdot 9.8066}

Next Step Evaluate

∴

v pm = 31.0008338597529m/s

LAST Step Rounding Answer

∴

v pm = 31.0008m/s

Initial Velocity given Maximum Horizontal Range 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

Maximum Horizontal Range

Maximum Horizontal Range is when the sine of two times of angle of projection in horizontal range tends to unity.

Symbol: H_max

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Maximum Horizontal Range

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

sqrt

A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number.

Syntax: sqrt(Number)

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 of Particle given Time of Flight of Projectile

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

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 given Maximum Horizontal Range of Projectile?

Initial Velocity given Maximum Horizontal Range of Projectile evaluator uses Initial Velocity of Projectile Motion = sqrt(Maximum Horizontal Range*[g]) to evaluate the Initial Velocity of Projectile Motion, Initial Velocity given Maximum Horizontal Range of Projectile formula is defined as a mathematical relationship that determines the initial velocity of a projectile when it is projected at an angle to achieve its maximum horizontal range, taking into account the gravitational force acting on the projectile. Initial Velocity of Projectile Motion is denoted by v_pm symbol.

How to evaluate Initial Velocity given Maximum Horizontal Range of Projectile using this online evaluator? To use this online evaluator for Initial Velocity given Maximum Horizontal Range of Projectile, enter Maximum Horizontal Range (H_max) and hit the calculate button.

FAQs on Initial Velocity given Maximum Horizontal Range of Projectile

What is the formula to find Initial Velocity given Maximum Horizontal Range of Projectile?

The formula of Initial Velocity given Maximum Horizontal Range of Projectile is expressed as Initial Velocity of Projectile Motion = sqrt(Maximum Horizontal Range*[g]). Here is an example- 31.00083 = sqrt(98*[g]).

How to calculate Initial Velocity given Maximum Horizontal Range of Projectile?

With Maximum Horizontal Range (H_max) we can find Initial Velocity given Maximum Horizontal Range of Projectile using the formula - Initial Velocity of Projectile Motion = sqrt(Maximum Horizontal Range*[g]). This formula also uses Gravitational acceleration on Earth constant(s) and Square Root Function 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=([g]*Time Interval)/(2*sin(Angle of Projection))

Can the Initial Velocity given Maximum Horizontal Range of Projectile be negative?

No, the Initial Velocity given Maximum Horizontal Range of Projectile, measured in Speed cannot be negative.

Which unit is used to measure Initial Velocity given Maximum Horizontal Range of Projectile?

Initial Velocity given Maximum Horizontal Range 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 given Maximum Horizontal Range of Projectile can be measured.

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