Height of Object given Horizontal Distance Calculator

✖Horizontal Distance denotes the instantaneous horizontal distance cover by an object in a projectile motion.ⓘ Horizontal Distance [R]			+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%
✖Acceleration due to Gravity is acceleration gained by an object because of gravitational force.ⓘ Acceleration due to Gravity [g]			+10% -10%
✖Initial Velocity is the velocity at which motion starts.ⓘ Initial Velocity [u]			+10% -10%

✖Height of Crack is the size of a flaw or crack in a material that can lead to catastrophic failure under a given stress.ⓘ Height of Object given Horizontal Distance [h]

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Formula

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Height of Object given Horizontal Distance

Formula

`"h" = "R"*tan("θ"_{"pr"})-("g"*"R"^2)/(2*("u"*cos("θ"_{"pr"}))^2)`

Example

`"826.7264mm"="2m"*tan("0.4rad")-("9.8m/s²"*("2m")^2)/(2*("35m/s"*cos("0.4rad"))^2)`

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Height of Object given Horizontal Distance Solution

STEP 0: Pre-Calculation Summary

Formula Used

Height of Crack = Horizontal Distance*tan(Angle of Projection)-(Acceleration due to Gravity*Horizontal Distance^2)/(2*(Initial Velocity*cos(Angle of Projection))^2)
h = R*tan(θ_pr)-(g*R^2)/(2*(u*cos(θ_pr))^2)
This formula uses 2 Functions, 5 Variables

Functions Used

cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., cos(Angle)
tan - The tangent of an angle is a trigonometric ratio of the length of the side opposite an angle to the length of the side adjacent to an angle in a right triangle., tan(Angle)

Variables Used

Height of Crack - (Measured in Meter) - Height of Crack is the size of a flaw or crack in a material that can lead to catastrophic failure under a given stress.
Horizontal Distance - (Measured in Meter) - Horizontal Distance denotes the instantaneous horizontal distance cover by an 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.
Acceleration due to Gravity - (Measured in Meter per Square Second) - Acceleration due to Gravity is acceleration gained by an object because of gravitational force.
Initial Velocity - (Measured in Meter per Second) - Initial Velocity is the velocity at which motion starts.

STEP 1: Convert Input(s) to Base Unit

Horizontal Distance: 2 Meter --> 2 Meter 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
Initial Velocity: 35 Meter per Second --> 35 Meter per Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

h = R*tan(θ_pr)-(g*R^2)/(2*(u*cos(θ_pr))^2) --> 2*tan(0.4)-(9.8*2^2)/(2*(35*cos(0.4))^2)

Evaluating ... ...

h = 0.826726371783348

STEP 3: Convert Result to Output's Unit

0.826726371783348 Meter -->826.726371783348 Millimeter (Check conversion here)

FINAL ANSWER

826.726371783348 ≈ 826.7264 Millimeter <-- Height of Crack

(Calculation completed in 00.004 seconds)

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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

Height of Object given Horizontal Distance Formula

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 Height of Object given Horizontal Distance?

Height of Object given Horizontal Distance calculator uses Height of Crack = Horizontal Distance*tan(Angle of Projection)-(Acceleration due to Gravity*Horizontal Distance^2)/(2*(Initial Velocity*cos(Angle of Projection))^2) to calculate the Height of Crack, The Height of Object given Horizontal Distance formula is obtained from the equation of trajectory. Height of Crack is denoted by h symbol.

How to calculate Height of Object given Horizontal Distance using this online calculator? To use this online calculator for Height of Object given Horizontal Distance, enter Horizontal Distance (R), Angle of Projection (θ_pr), Acceleration due to Gravity (g) & Initial Velocity (u) and hit the calculate button. Here is how the Height of Object given Horizontal Distance calculation can be explained with given input values -> 418078.2 = 2*tan(0.4)-(9.8*2^2)/(2*(35*cos(0.4))^2).

FAQ

What is Height of Object given Horizontal Distance?

The Height of Object given Horizontal Distance formula is obtained from the equation of trajectory and is represented as h = R*tan(θ_pr)-(g*R^2)/(2*(u*cos(θ_pr))^2) or Height of Crack = Horizontal Distance*tan(Angle of Projection)-(Acceleration due to Gravity*Horizontal Distance^2)/(2*(Initial Velocity*cos(Angle of Projection))^2). Horizontal Distance denotes the instantaneous horizontal distance cover by an object in a projectile motion, Angle of Projection is angle made by the particle with horizontal when projected upwards with some initial velocity, Acceleration due to Gravity is acceleration gained by an object because of gravitational force & Initial Velocity is the velocity at which motion starts.

How to calculate Height of Object given Horizontal Distance?

The Height of Object given Horizontal Distance formula is obtained from the equation of trajectory is calculated using Height of Crack = Horizontal Distance*tan(Angle of Projection)-(Acceleration due to Gravity*Horizontal Distance^2)/(2*(Initial Velocity*cos(Angle of Projection))^2). To calculate Height of Object given Horizontal Distance, you need Horizontal Distance (R), Angle of Projection (θ_pr), Acceleration due to Gravity (g) & Initial Velocity (u). With our tool, you need to enter the respective value for Horizontal Distance, Angle of Projection, Acceleration due to Gravity & Initial Velocity 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 Height of Crack?

In this formula, Height of Crack uses Horizontal Distance, Angle of Projection, Acceleration due to Gravity & Initial Velocity. We can use 1 other way(s) to calculate the same, which is/are as follows -

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

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