Initial Velocity using Range Calculator

✖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 Motion [R_motion]			+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%

✖Initial Velocity is the velocity of an object at the start of a motion, describing the object's initial state of motion.ⓘ Initial Velocity using Range [u]

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Initial Velocity using Range Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Variables Used

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.
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.
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.
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.

STEP 1: Convert Input(s) to Base Unit

Acceleration due to Gravity: 9.8 Meter per Square Second --> 9.8 Meter per Square Second No Conversion Required
Range of Motion: 89.66951 Meter --> 89.66951 Meter No Conversion Required
Angle of Projection: 0.4 Radian --> 0.4 Radian No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

u = sqrt(g*R_motion/sin(2*θ_pr)) --> sqrt(9.8*89.66951/sin(2*0.4))

Evaluating ... ...

u = 34.9999997341046

STEP 3: Convert Result to Output's Unit

34.9999997341046 Meter per Second --> No Conversion Required

FINAL ANSWER

34.9999997341046 ≈ 35 Meter per Second <-- Initial Velocity

(Calculation completed in 00.021 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)

Initial Velocity using Range Formula

LaTeX Go

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

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 Initial Velocity using Range?

Initial Velocity using Range calculator uses Initial Velocity = sqrt(Acceleration due to Gravity*Range of Motion/sin(2*Angle of Projection)) to calculate 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 calculate Initial Velocity using Range using this online calculator? To use this online calculator 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. Here is how the Initial Velocity using Range calculation can be explained with given input values -> 11.97679 = sqrt(9.8*89.66951/sin(2*0.4)).

FAQ

What is Initial Velocity using Range?

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 and is represented as u = sqrt(g*R_motion/sin(2*θ_pr)) or Initial Velocity = sqrt(Acceleration due to Gravity*Range of Motion/sin(2*Angle of Projection)). 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, 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 & Angle of Projection is the angle at which an object is projected from the ground, influencing its trajectory and range of motion.

How to calculate Initial Velocity using Range?

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 is calculated using Initial Velocity = sqrt(Acceleration due to Gravity*Range of Motion/sin(2*Angle of Projection)). To calculate Initial Velocity using Range, you need Acceleration due to Gravity (g), Range of Motion (R_motion) & Angle of Projection (θ_pr). With our tool, you need to enter the respective value for Acceleration due to Gravity, Range of Motion & Angle of Projection 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 Initial Velocity?

In this formula, Initial Velocity uses Acceleration due to Gravity, Range of Motion & Angle of Projection. We can use 2 other way(s) to calculate the same, which is/are as follows -

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)

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