Maximum Height of Projectile on Horizontal Plane Solution

STEP 0: Pre-Calculation Summary
Formula Used
Maximum Height = (Initial Velocity of Projectile Motion^2*sin(Angle of Projection)^2)/(2*[g])
hmax = (vpm^2*sin(αpr)^2)/(2*[g])
This formula uses 1 Constants, 1 Functions, 3 Variables
Constants Used
[g] - Gravitational acceleration on Earth Value Taken As 9.80665
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
Maximum Height - (Measured in Meter) - Maximum Height is denoted as the largest distance an object covers in vertical direction in a projectile motion.
Initial Velocity of Projectile Motion - (Measured in Meter per Second) - Initial Velocity of Projectile Motion is the velocity at which motion starts.
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
Initial Velocity of Projectile Motion: 30.01 Meter per Second --> 30.01 Meter per Second No Conversion Required
Angle of Projection: 44.99 Degree --> 0.785223630472101 Radian (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
hmax = (vpm^2*sin(αpr)^2)/(2*[g]) --> (30.01^2*sin(0.785223630472101)^2)/(2*[g])
Evaluating ... ...
hmax = 22.9508989121245
STEP 3: Convert Result to Output's Unit
22.9508989121245 Meter --> No Conversion Required
FINAL ANSWER
22.9508989121245 22.9509 Meter <-- Maximum Height
(Calculation completed in 00.004 seconds)

Credits

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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14 Projectile Motion Calculators

Direction of Projectile at given Height above Point of Projection
Go Direction of Motion of a Particle = atan((sqrt((Initial Velocity of Projectile Motion^2*(sin(Angle of Projection))^2)-2*[g]*Height))/(Initial Velocity of Projectile Motion*cos(Angle of Projection)))
Maximum Height of Projectile on Horizontal Plane
Go Maximum Height = (Initial Velocity of Projectile Motion^2*sin(Angle of Projection)^2)/(2*[g])
Horizontal Range of Projectile
Go Horizontal Range = (Initial Velocity of Projectile Motion^2*sin(2*Angle of Projection))/[g]
Initial Velocity of Particle given Time of Flight of Projectile
Go Initial Velocity of Projectile Motion = ([g]*Time Interval)/(2*sin(Angle of Projection))
Time of Flight of Projectile on Horizontal Plane
Go Time Interval = (2*Initial Velocity of Projectile Motion*sin(Angle of Projection))/[g]
Velocity of Projectile at given Height above Point of Projection
Go Velocity of Projectile = sqrt(Initial Velocity of Projectile Motion^2-2*[g]*Height)
Horizontal Component of Velocity of Particle Projected Upwards from Point at Angle
Go Horizontal Component of Velocity = Initial Velocity of Projectile Motion*cos(Angle of Projection)
Initial Velocity of Particle given Horizontal Component of Velocity
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
Go Vertical Component of Velocity = Initial Velocity of Projectile Motion*sin(Angle of Projection)
Initial Velocity of Particle given Vertical Component of Velocity
Go Initial Velocity of Projectile Motion = Vertical Component of Velocity/sin(Angle of Projection)
Initial Velocity given Maximum Horizontal Range of Projectile
Go Initial Velocity of Projectile Motion = sqrt(Maximum Horizontal Range*[g])
Horizontal Range of Projectile given Horizontal Velocity and Time of Flight
Go Horizontal Range = Horizontal Component of Velocity*Time Interval
Maximum Horizontal Range of Projectile
Go Horizontal Range = Initial Velocity of Projectile Motion^2/[g]
Maximum Height of Projectile on Horizontal Plane given Average Vertical Velocity
Go Maximum Height = Average Vertical Velocity*Time Interval

Maximum Height of Projectile on Horizontal Plane Formula

Maximum Height = (Initial Velocity of Projectile Motion^2*sin(Angle of Projection)^2)/(2*[g])
hmax = (vpm^2*sin(αpr)^2)/(2*[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 Maximum Height of Projectile on Horizontal Plane?

Maximum Height of Projectile on Horizontal Plane calculator uses Maximum Height = (Initial Velocity of Projectile Motion^2*sin(Angle of Projection)^2)/(2*[g]) to calculate the Maximum Height, The Maximum height of projectile on horizontal plane formula is defined as the ratio of product of square of initial velocity and square of sine of angle of projection to the two times of acceleration due to gravity. Maximum Height is denoted by hmax symbol.

How to calculate Maximum Height of Projectile on Horizontal Plane using this online calculator? To use this online calculator for Maximum Height of Projectile on Horizontal Plane, enter Initial Velocity of Projectile Motion (vpm) & Angle of Projection pr) and hit the calculate button. Here is how the Maximum Height of Projectile on Horizontal Plane calculation can be explained with given input values -> 22.95891 = (30.01^2*sin(0.785223630472101)^2)/(2*[g]).

FAQ

What is Maximum Height of Projectile on Horizontal Plane?
The Maximum height of projectile on horizontal plane formula is defined as the ratio of product of square of initial velocity and square of sine of angle of projection to the two times of acceleration due to gravity and is represented as hmax = (vpm^2*sin(αpr)^2)/(2*[g]) or Maximum Height = (Initial Velocity of Projectile Motion^2*sin(Angle of Projection)^2)/(2*[g]). Initial Velocity of Projectile Motion is the velocity at which motion starts & Angle of Projection is angle made by the particle with horizontal when projected upwards with some initial velocity.
How to calculate Maximum Height of Projectile on Horizontal Plane?
The Maximum height of projectile on horizontal plane formula is defined as the ratio of product of square of initial velocity and square of sine of angle of projection to the two times of acceleration due to gravity is calculated using Maximum Height = (Initial Velocity of Projectile Motion^2*sin(Angle of Projection)^2)/(2*[g]). To calculate Maximum Height of Projectile on Horizontal Plane, you need Initial Velocity of Projectile Motion (vpm) & Angle of Projection pr). With our tool, you need to enter the respective value for Initial Velocity of Projectile 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 Maximum Height?
In this formula, Maximum Height uses Initial Velocity of Projectile Motion & Angle of Projection. We can use 1 other way(s) to calculate the same, which is/are as follows -
  • Maximum Height = Average Vertical Velocity*Time Interval
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