Range of Projectile Motion 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 Projection is the angle at which an object is projected from the ground, influencing its trajectory and range of motion.ⓘ Angle of Projection [θ_pr]			+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.ⓘ Range of Projectile Motion [R_motion]

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Range of Projectile Motion Solution

STEP 0: Pre-Calculation Summary

Formula Used

Range of Motion = (Initial Velocity^2*sin(2*Angle of Projection))/Acceleration due to Gravity
R_motion = (u^2*sin(2*θ_pr))/g
This formula uses 1 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)

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 Projection - (Measured in Radian) - Angle of Projection is the angle at which an object is projected from the ground, influencing its trajectory and range of motion.
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 Projection: 0.4 Radian --> 0.4 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*sin(2*θ_pr))/g --> (35^2*sin(2*0.4))/9.8

Evaluating ... ...

R_motion = 89.6695113624403

STEP 3: Convert Result to Output's Unit

89.6695113624403 Meter --> No Conversion Required

FINAL ANSWER

89.6695113624403 ≈ 89.66951 Meter <-- Range of Motion

(Calculation completed in 00.020 seconds)

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Created by Himanshi Sharma

Bhilai Institute of Technology (BIT), Raipur

Himanshi Sharma has created this Calculator and 4 more calculators!

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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)

Range of Projectile Motion Formula

LaTeX Go

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

What is Projectile Motion ?

Projectile motion is a type of two-dimensional motion or motion in a plane. It is assumed that the only force acting on a projectile (the object experiencing projectile motion) is the force due to gravity.

How to Calculate Range of Projectile Motion?

Range of Projectile Motion calculator uses Range of Motion = (Initial Velocity^2*sin(2*Angle of Projection))/Acceleration due to Gravity to calculate 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 calculate Range of Projectile Motion using this online calculator? To use this online calculator for Range of Projectile Motion, enter Initial Velocity (u), Angle of Projection (θ_pr) & Acceleration due to Gravity (g) and hit the calculate button. Here is how the Range of Projectile Motion calculation can be explained with given input values -> 89.66951 = (35^2*sin(2*0.4))/9.8.

FAQ

What is Range of Projectile 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 and is represented as R_motion = (u^2*sin(2*θ_pr))/g or Range of Motion = (Initial Velocity^2*sin(2*Angle of Projection))/Acceleration due to Gravity. Initial Velocity is the velocity of an object at the start of a motion, describing the object's initial state of motion, Angle of Projection is the angle at which an object is projected from the ground, influencing its trajectory and range of motion & 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 Range of Projectile 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 is calculated using Range of Motion = (Initial Velocity^2*sin(2*Angle of Projection))/Acceleration due to Gravity. To calculate Range of Projectile Motion, you need Initial Velocity (u), Angle of Projection (θ_pr) & Acceleration due to Gravity (g). With our tool, you need to enter the respective value for Initial Velocity, Angle of Projection & 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 Projection & 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*(1-sin(Angle of Plane)))/(Acceleration due to Gravity*(cos(Angle of Plane))^2)

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