Initial Velocity using Range Calculator

✖Acceleration due to Gravity is acceleration gained by an object because of gravitational force.ⓘ Acceleration due to Gravity [g]			+10% -10%
✖Range of Motion is defined as the total horizontal distance travelled by the object in a projectile motion.ⓘ Range of Motion [R_motion]			+10% -10%
✖Angle of Projection is angle made by the particle with horizontal when projected upwards with some initial velocity.ⓘ Angle of Projection [θ_pr]			+10% -10%

✖Initial Velocity is the velocity at which motion starts.ⓘ Initial Velocity using Range [u]

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Formula

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Initial Velocity using Range

Formula

`"u" = sqrt("g"*"R"_{"motion"}/sin(2*"θ"_{"pr"}))`

Example

`"11.97679m/s"=sqrt("9.8m/s²"*"10.5m"/sin(2*"0.4rad"))`

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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 at which motion starts.
Acceleration due to Gravity - (Measured in Meter per Square Second) - Acceleration due to Gravity is acceleration gained by an object because of gravitational force.
Range of Motion - (Measured in Meter) - Range of Motion is defined as the total horizontal distance travelled by the object in a projectile motion.
Angle of Projection - (Measured in Radian) - Angle of Projection is angle made by the particle with horizontal when projected upwards with some initial velocity.

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: 10.5 Meter --> 10.5 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*10.5/sin(2*0.4))

Evaluating ... ...

u = 11.9767860720266

STEP 3: Convert Result to Output's Unit

11.9767860720266 Meter per Second --> No Conversion Required

FINAL ANSWER

11.9767860720266 ≈ 11.97679 Meter per Second <-- Initial Velocity

(Calculation completed in 00.004 seconds)

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Created by Himanshi Sharma

Bhilai Institute of Technology (BIT), Raipur

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< 7 Projectile Motion ( object thrown at some angle 'theta' ) Calculators

Height of Object given Horizontal Distance

Go Height of Crack = Horizontal Distance*tan(Angle of Projection)-(Acceleration due to Gravity*Horizontal Distance^2)/(2*(Initial Velocity*cos(Angle of Projection))^2)

Initial Speed given Maximum Height

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

Initial Velocity using Range

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

Maximum Height Attained by Object

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

Range of Projectile Motion

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

Initial Speed using Time of Flight

Go Initial Velocity = (Time of Flight*Acceleration due to Gravity)/(2*sin(Angle of Projection))

Time of Flight

Go Time of Flight = (2*Initial Velocity*sin(Angle of Projection))/Acceleration due to Gravity

Initial Velocity using Range Formula

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, The Initial Velocity using Range formula is defined as the velocity with which the body is projected(resultant of its horizontal and vertical velocity). 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*10.5/sin(2*0.4)).

FAQ

What is Initial Velocity using Range?

The Initial Velocity using Range formula is defined as the velocity with which the body is projected(resultant of its horizontal and vertical velocity) 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 acceleration gained by an object because of gravitational force, Range of Motion is defined as the total horizontal distance travelled by the object in a projectile motion & Angle of Projection is angle made by the particle with horizontal when projected upwards with some initial velocity.

How to calculate Initial Velocity using Range?

The Initial Velocity using Range formula is defined as the velocity with which the body is projected(resultant of its horizontal and vertical velocity) 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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