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Range of Projectile Motion Formula

GoMaximum Range of Flight for Inclined Projectile Formula

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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. Check FAQs

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

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

Range of Projectile Motion Example

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Here is how the Range of Projectile Motion equation looks like with Values.

Here is how the Range of Projectile Motion equation looks like with Units.

Here is how the Range of Projectile Motion equation looks like.

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

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

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

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Range of Projectile Motion Solution

Follow our step by step solution on how to calculate Range of Projectile Motion?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

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

Next Step Prepare to Evaluate

∴

R motion = \frac{35^{2} \cdot \sin (2 \cdot 0.4)}{9.8}

Next Step Evaluate

∴

R motion = 89.6695113624403m

LAST Step Rounding Answer

∴

R motion = 89.6695m

Range of Projectile Motion Formula Elements

Variables

Functions

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

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

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

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

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 Range of Motion

Go Maximum Range of Flight for Inclined Projectile

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

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 Height Attained by Object

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

Go Time of Flight

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

How to Evaluate Range of Projectile Motion?

Range of Projectile Motion evaluator uses Range of Motion = (Initial Velocity^2*sin(2*Angle of Projection))/Acceleration due to Gravity to evaluate the Range of Motion, Range of Projectile Motion formula is defined as the maximum horizontal distance a projectile can travel under the sole influence of gravity, dependent on the initial velocity and angle of projection, providing a fundamental concept in understanding the kinematics of motion. Range of Motion is denoted by R_motion symbol.

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

FAQs on Range of Projectile Motion

What is the formula to find Range of Projectile Motion?

The formula of Range of Projectile Motion is expressed as Range of Motion = (Initial Velocity^2*sin(2*Angle of Projection))/Acceleration due to Gravity. Here is an example- 89.66951 = (35^2*sin(2*0.4))/9.8.

How to calculate Range of Projectile Motion?

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

What are the other ways to Calculate Range of Motion?

Here are the different ways to Calculate Range of Motion-

Range of Motion=(Initial Velocity^2*(1-sin(Angle of Plane)))/(Acceleration due to Gravity*(cos(Angle of Plane))^2)

Can the Range of Projectile Motion be negative?

Yes, the Range of Projectile Motion, measured in Length can be negative.

Which unit is used to measure Range of Projectile Motion?

Range of Projectile Motion is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Range of Projectile Motion can be measured.

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