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Maximum Range of Flight for Inclined Projectile Formula

GoRange of Projectile Motion 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 (1 - \sin (α pl))}{g \cdot {(\cos (α pl))}^{2}}

R_motion - Range of Motion?u - Initial Velocity?α_pl - Angle of Plane?g - Acceleration due to Gravity?

Maximum Range of Flight for Inclined Projectile Example

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Here is how the Maximum Range of Flight for Inclined Projectile equation looks like with Values.

Here is how the Maximum Range of Flight for Inclined Projectile equation looks like with Units.

Here is how the Maximum Range of Flight for Inclined Projectile equation looks like.

89.6688 = \frac{35^{2} \cdot (1 - \sin (0.405))}{9.8 \cdot {(\cos (0.405))}^{2}}

89.6688m = \frac{{35m/s}^{2} \cdot (1 - \sin (0.405rad))}{9.8m/s² \cdot {(\cos (0.405rad))}^{2}}

89.6688 = \frac{35^{2} \cdot (1 - \sin (0.405))}{9.8 \cdot {(\cos (0.405))}^{2}}

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Maximum Range of Flight for Inclined Projectile Solution

Follow our step by step solution on how to calculate Maximum Range of Flight for Inclined Projectile?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

R motion = \frac{{35m/s}^{2} \cdot (1 - \sin (0.405rad))}{9.8m/s² \cdot {(\cos (0.405rad))}^{2}}

Next Step Prepare to Evaluate

∴

R motion = \frac{35^{2} \cdot (1 - \sin (0.405))}{9.8 \cdot {(\cos (0.405))}^{2}}

Next Step Evaluate

∴

R motion = 89.6688075896142m

LAST Step Rounding Answer

∴

R motion = 89.6688m

Maximum Range of Flight for Inclined Projectile 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 Plane

Angle of Plane is the angle between the plane of motion and the horizontal plane, measured in a clockwise direction from the horizontal plane.

Symbol: α_pl

Measurement: AngleUnit: rad

Note: Value can be positive or negative.

Formulas to find Angle of Plane

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)

cos

Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle.

Syntax: cos(Angle)

Other Formulas to find Range of Motion

Go Range of Projectile Motion

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

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 Maximum Range of Flight for Inclined Projectile?

Maximum Range of Flight for Inclined Projectile evaluator uses Range of Motion = (Initial Velocity^2*(1-sin(Angle of Plane)))/(Acceleration due to Gravity*(cos(Angle of Plane))^2) to evaluate the Range of Motion, Maximum Range of Flight for Inclined Projectile formula is defined as the maximum horizontal distance that an object can travel when projected at an angle to the horizontal, taking into account the initial velocity, angle of projection, and acceleration due to gravity. Range of Motion is denoted by R_motion symbol.

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

FAQs on Maximum Range of Flight for Inclined Projectile

What is the formula to find Maximum Range of Flight for Inclined Projectile?

The formula of Maximum Range of Flight for Inclined Projectile is expressed as Range of Motion = (Initial Velocity^2*(1-sin(Angle of Plane)))/(Acceleration due to Gravity*(cos(Angle of Plane))^2). Here is an example- 68.10219 = (35^2*(1-sin(0.405)))/(9.8*(cos(0.405))^2).

How to calculate Maximum Range of Flight for Inclined Projectile?

With Initial Velocity (u), Angle of Plane (α_pl) & Acceleration due to Gravity (g) we can find Maximum Range of Flight for Inclined Projectile using the formula - Range of Motion = (Initial Velocity^2*(1-sin(Angle of Plane)))/(Acceleration due to Gravity*(cos(Angle of Plane))^2). This formula also uses Sine (sin), Cosine (cos) 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*sin(2*Angle of Projection))/Acceleration due to Gravity

Can the Maximum Range of Flight for Inclined Projectile be negative?

Yes, the Maximum Range of Flight for Inclined Projectile, measured in Length can be negative.

Which unit is used to measure Maximum Range of Flight for Inclined Projectile?

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

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