Maximum Range of Flight for Inclined Projectile Calculator

✖Initial Velocity is the velocity of an object at the start of a motion, describing the object's initial state of motion.ⓘ Initial Velocity [u]			+10% -10%
✖Angle of Plane is the angle between the plane of motion and the horizontal plane, measured in a clockwise direction from the horizontal plane.ⓘ Angle of Plane [α_pl]			+10% -10%
✖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.ⓘ Acceleration due to Gravity [g]			+10% -10%

✖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.ⓘ Maximum Range of Flight for Inclined Projectile [R_motion]

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Maximum Range of Flight for Inclined Projectile Solution

STEP 0: Pre-Calculation Summary

Formula Used

Range of Motion = (Initial Velocity^2*(1-sin(Angle of Plane)))/(Acceleration due to Gravity*(cos(Angle of Plane))^2)
R_motion = (u^2*(1-sin(α_pl)))/(g*(cos(α_pl))^2)
This formula uses 2 Functions, 4 Variables

Functions Used

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., sin(Angle)
cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., cos(Angle)

Variables Used

Range of Motion - (Measured in Meter) - 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.
Initial Velocity - (Measured in Meter per Second) - Initial Velocity is the velocity of an object at the start of a motion, describing the object's initial state of motion.
Angle of Plane - (Measured in Radian) - Angle of Plane is the angle between the plane of motion and the horizontal plane, measured in a clockwise direction from the horizontal plane.
Acceleration due to Gravity - (Measured in Meter per Square Second) - 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.

STEP 1: Convert Input(s) to Base Unit

Initial Velocity: 35 Meter per Second --> 35 Meter per Second No Conversion Required
Angle of Plane: 0.405 Radian --> 0.405 Radian No Conversion Required
Acceleration due to Gravity: 9.8 Meter per Square Second --> 9.8 Meter per Square Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

R_motion = (u^2*(1-sin(α_pl)))/(g*(cos(α_pl))^2) --> (35^2*(1-sin(0.405)))/(9.8*(cos(0.405))^2)

Evaluating ... ...

R_motion = 89.6688075896142

STEP 3: Convert Result to Output's Unit

89.6688075896142 Meter --> No Conversion Required

FINAL ANSWER

89.6688075896142 ≈ 89.66881 Meter <-- Range of Motion

(Calculation completed in 00.004 seconds)

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Created by Mayank Tayal

National Institute of Technology (NIT), Durgapur

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National Institute Of Technology (NIT), Hamirpur

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< Projectile Motion Calculators

Maximum Height Attained for Inclined Projectile

LaTeX Go Maximum Height = ((Initial Velocity*sin(Angle of Inclination))^2)/(2*Acceleration due to Gravity*cos(Angle of Plane))

Maximum Range of Flight for Inclined Projectile

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

Time of Flight for Inclined Projectile

LaTeX Go Time of Flight = (2*Initial Velocity*sin(Angle of Inclination))/(Acceleration due to Gravity*cos(Angle of Plane))

Maximum Height Attained by Object

LaTeX Go Maximum Height of Crack = ((Initial Velocity*sin(Angle of Projection))^2)/(2*Acceleration due to Gravity)

Maximum Range of Flight for Inclined Projectile Formula

LaTeX Go

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

What is Inclined Projectile Motion ?

Projectile motion on an inclined plane is one of the various projectile motion types. The main distinguishing aspect is that points of projection and return are not on the same horizontal plane. There are two possibilities : (i) the point of return is at a higher level than the point of projection i.e projectile is thrown up the incline and (ii) the Point of return is at a lower level than a point of projection i.e. projectile is thrown down the incline.

How to Calculate Maximum Range of Flight for Inclined Projectile?

Maximum Range of Flight for Inclined Projectile calculator uses Range of Motion = (Initial Velocity^2*(1-sin(Angle of Plane)))/(Acceleration due to Gravity*(cos(Angle of Plane))^2) to calculate 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 calculate Maximum Range of Flight for Inclined Projectile using this online calculator? To use this online calculator 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. Here is how the Maximum Range of Flight for Inclined Projectile calculation can be explained with given input values -> 68.10219 = (35^2*(1-sin(0.405)))/(9.8*(cos(0.405))^2).

FAQ

What is Maximum Range of Flight for Inclined Projectile?

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 and is represented as R_motion = (u^2*(1-sin(α_pl)))/(g*(cos(α_pl))^2) or Range of Motion = (Initial Velocity^2*(1-sin(Angle of Plane)))/(Acceleration due to Gravity*(cos(Angle of Plane))^2). Initial Velocity is the velocity of an object at the start of a motion, describing the object's initial state of motion, Angle of Plane is the angle between the plane of motion and the horizontal plane, measured in a clockwise direction from the horizontal plane & 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.

How to calculate Maximum Range of Flight for Inclined Projectile?

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 is calculated using Range of Motion = (Initial Velocity^2*(1-sin(Angle of Plane)))/(Acceleration due to Gravity*(cos(Angle of Plane))^2). To calculate Maximum Range of Flight for Inclined Projectile, you need Initial Velocity (u), Angle of Plane (α_pl) & Acceleration due to Gravity (g). With our tool, you need to enter the respective value for Initial Velocity, Angle of Plane & Acceleration due to Gravity and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Range of Motion?

In this formula, Range of Motion uses Initial Velocity, Angle of Plane & Acceleration due to Gravity. We can use 1 other way(s) to calculate the same, which is/are as follows -

Range of Motion = (Initial Velocity^2*sin(2*Angle of Projection))/Acceleration due to Gravity

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