Initial Velocity given Maximum Horizontal Range of Projectile Calculator

✖Maximum Horizontal Range is when the sine of two times of angle of projection in horizontal range tends to unity.ⓘ Maximum Horizontal Range [H_max]

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✖Initial Velocity of Projectile Motion is the velocity at which motion starts.ⓘ Initial Velocity given Maximum Horizontal Range of Projectile [v_pm]

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Initial Velocity given Maximum Horizontal Range of Projectile Solution

STEP 0: Pre-Calculation Summary

Formula Used

Initial Velocity of Projectile Motion = sqrt(Maximum Horizontal Range*[g])
v_pm = sqrt(H_max*[g])
This formula uses 1 Constants, 1 Functions, 2 Variables

Constants Used

[g] - Gravitational acceleration on Earth Value Taken As 9.80665

Functions Used

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 of Projectile Motion - (Measured in Meter per Second) - Initial Velocity of Projectile Motion is the velocity at which motion starts.
Maximum Horizontal Range - (Measured in Meter) - Maximum Horizontal Range is when the sine of two times of angle of projection in horizontal range tends to unity.

STEP 1: Convert Input(s) to Base Unit

Maximum Horizontal Range: 98 Meter --> 98 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

v_pm = sqrt(H_max*[g]) --> sqrt(98*[g])

Evaluating ... ...

v_pm = 31.0008338597529

STEP 3: Convert Result to Output's Unit

31.0008338597529 Meter per Second --> No Conversion Required

FINAL ANSWER

31.0008338597529 ≈ 31.00083 Meter per Second <-- Initial Velocity of Projectile Motion

(Calculation completed in 00.020 seconds)

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Created by Chilvera Bhanu Teja

Institute of Aeronautical Engineering (IARE), Hyderabad

Chilvera Bhanu Teja has created this Calculator and 300+ more calculators!

Verified by Rajat Vishwakarma

University Institute of Technology RGPV (UIT - RGPV), Bhopal

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< Projectile Motion Calculators

Horizontal Component of Velocity of Particle Projected Upwards from Point at Angle

LaTeX Go Horizontal Component of Velocity = Initial Velocity of Projectile Motion*cos(Angle of Projection)

Initial Velocity of Particle given Horizontal Component of Velocity

LaTeX Go Initial Velocity of Projectile Motion = Horizontal Component of Velocity/cos(Angle of Projection)

Vertical Component of Velocity of Particle Projected Upwards from Point at Angle

LaTeX Go Vertical Component of Velocity = Initial Velocity of Projectile Motion*sin(Angle of Projection)

Initial Velocity of Particle given Vertical Component of Velocity

LaTeX Go Initial Velocity of Projectile Motion = Vertical Component of Velocity/sin(Angle of Projection)

Initial Velocity given Maximum Horizontal Range of Projectile Formula

LaTeX Go

Initial Velocity of Projectile Motion = sqrt(Maximum Horizontal Range*[g])
v_pm = sqrt(H_max*[g])

What is projectile motion?

When a particle is thrown obliquely near the earth’s surface, it moves along a curved path under constant acceleration that is directed towards the center of the earth (we assume that the particle remains close to the surface of the earth). The path of such a particle is called a projectile and the motion is called projectile motion.

How to Calculate Initial Velocity given Maximum Horizontal Range of Projectile?

Initial Velocity given Maximum Horizontal Range of Projectile calculator uses Initial Velocity of Projectile Motion = sqrt(Maximum Horizontal Range*[g]) to calculate the Initial Velocity of Projectile Motion, Initial Velocity given Maximum Horizontal Range of Projectile formula is defined as a mathematical relationship that determines the initial velocity of a projectile when it is projected at an angle to achieve its maximum horizontal range, taking into account the gravitational force acting on the projectile. Initial Velocity of Projectile Motion is denoted by v_pm symbol.

How to calculate Initial Velocity given Maximum Horizontal Range of Projectile using this online calculator? To use this online calculator for Initial Velocity given Maximum Horizontal Range of Projectile, enter Maximum Horizontal Range (H_max) and hit the calculate button. Here is how the Initial Velocity given Maximum Horizontal Range of Projectile calculation can be explained with given input values -> 31.00083 = sqrt(98*[g]).

FAQ

What is Initial Velocity given Maximum Horizontal Range of Projectile?

Initial Velocity given Maximum Horizontal Range of Projectile formula is defined as a mathematical relationship that determines the initial velocity of a projectile when it is projected at an angle to achieve its maximum horizontal range, taking into account the gravitational force acting on the projectile and is represented as v_pm = sqrt(H_max*[g]) or Initial Velocity of Projectile Motion = sqrt(Maximum Horizontal Range*[g]). Maximum Horizontal Range is when the sine of two times of angle of projection in horizontal range tends to unity.

How to calculate Initial Velocity given Maximum Horizontal Range of Projectile?

Initial Velocity given Maximum Horizontal Range of Projectile formula is defined as a mathematical relationship that determines the initial velocity of a projectile when it is projected at an angle to achieve its maximum horizontal range, taking into account the gravitational force acting on the projectile is calculated using Initial Velocity of Projectile Motion = sqrt(Maximum Horizontal Range*[g]). To calculate Initial Velocity given Maximum Horizontal Range of Projectile, you need Maximum Horizontal Range (H_max). With our tool, you need to enter the respective value for Maximum Horizontal Range 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 of Projectile Motion?

In this formula, Initial Velocity of Projectile Motion uses Maximum Horizontal Range. We can use 3 other way(s) to calculate the same, which is/are as follows -

Initial Velocity of Projectile Motion = Horizontal Component of Velocity/cos(Angle of Projection)
Initial Velocity of Projectile Motion = Vertical Component of Velocity/sin(Angle of Projection)
Initial Velocity of Projectile Motion = ([g]*Time Interval)/(2*sin(Angle of Projection))

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