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Initial Velocity using Range Formula

GoInitial Speed using Time of Flight Formula

GoInitial Speed given Maximum Height 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 = \sqrt{g \cdot \frac{R motion}{\sin (2 \cdot θ pr)}}

u - Initial Velocity?g - Acceleration due to Gravity?R_motion - Range of Motion?θ_pr - Angle of Projection?

Initial Velocity using Range Example

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Here is how the Initial Velocity using Range equation looks like with Values.

Here is how the Initial Velocity using Range equation looks like with Units.

Here is how the Initial Velocity using Range equation looks like.

35 = \sqrt{9.8 \cdot \frac{89.6695}{\sin (2 \cdot 0.4)}}

35m/s = \sqrt{9.8m/s² \cdot \frac{89.6695m}{\sin (2 \cdot 0.4rad)}}

35 = \sqrt{9.8 \cdot \frac{89.6695}{\sin (2 \cdot 0.4)}}

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Initial Velocity using Range Solution

Follow our step by step solution on how to calculate Initial Velocity using Range?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

u = \sqrt{9.8m/s² \cdot \frac{89.6695m}{\sin (2 \cdot 0.4rad)}}

Next Step Prepare to Evaluate

∴

u = \sqrt{9.8 \cdot \frac{89.6695}{\sin (2 \cdot 0.4)}}

Next Step Evaluate

∴

u = 34.9999997341046m/s

LAST Step Rounding Answer

∴

u = 35m/s

Initial Velocity using Range 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

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

Range of Motion

Range of Motion is the measure of the extent of movement of a joint or a limb in a specific direction or plane of motion.

Symbol: R_motion

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Range of Motion

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)

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

Go Initial Speed using Time of Flight

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

Go Initial Speed given Maximum Height

u = \frac{\sqrt{H max \cdot 2 \cdot g}}{\sin (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 Velocity using Range?

Initial Velocity using Range evaluator uses Initial Velocity = sqrt(Acceleration due to Gravity*Range of Motion/sin(2*Angle of Projection)) to evaluate the Initial Velocity, Initial Velocity using Range formula is defined as the velocity of an object at the start of its motion, which is a crucial parameter in understanding the kinematics of motion, particularly in describing the trajectory of projectiles under the influence of gravity. Initial Velocity is denoted by u symbol.

How to evaluate Initial Velocity using Range using this online evaluator? To use this online evaluator for Initial Velocity using Range, enter Acceleration due to Gravity (g), Range of Motion (R_motion) & Angle of Projection (θ_pr) and hit the calculate button.

FAQs on Initial Velocity using Range

What is the formula to find Initial Velocity using Range?

The formula of Initial Velocity using Range is expressed as Initial Velocity = sqrt(Acceleration due to Gravity*Range of Motion/sin(2*Angle of Projection)). Here is an example- 11.97679 = sqrt(9.8*89.66951/sin(2*0.4)).

How to calculate Initial Velocity using Range?

With Acceleration due to Gravity (g), Range of Motion (R_motion) & Angle of Projection (θ_pr) we can find Initial Velocity using Range using the formula - Initial Velocity = sqrt(Acceleration due to Gravity*Range of Motion/sin(2*Angle of Projection)). This formula also uses Sine (sin), Square Root (sqrt) function(s).

What are the other ways to Calculate Initial Velocity?

Here are the different ways to Calculate Initial Velocity-

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

Can the Initial Velocity using Range be negative?

No, the Initial Velocity using Range, measured in Speed cannot be negative.

Which unit is used to measure Initial Velocity using Range?

Initial Velocity using Range 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 using Range can be measured.

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