Direction of Projectile at given Height above Point of Projection Calculator

✖Initial Velocity of Projectile Motion is the velocity at which motion starts.ⓘ Initial Velocity of Projectile Motion [v_pm]			+10% -10%
✖Angle of Projection is angle made by the particle with horizontal when projected upwards with some initial velocity.ⓘ Angle of Projection [α_pr]			+10% -10%
✖Height is the distance between the lowest and highest points of a person/ shape/ object standing upright.ⓘ Height [h]			+10% -10%

✖Direction of Motion of a Particle is angle which the projectile makes with the horizontal.ⓘ Direction of Projectile at given Height above Point of Projection [θ_pr]

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Direction of Projectile at given Height above Point of Projection Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)))
θ_pr = atan((sqrt((v_pm^2*(sin(α_pr))^2)-2*[g]*h))/(v_pm*cos(α_pr)))
This formula uses 1 Constants, 5 Functions, 4 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)
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)
atan - Inverse tan is used to calculate the angle by applying the tangent ratio of the angle, which is the opposite side divided by the adjacent side of the right triangle., atan(Number)
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

Direction of Motion of a Particle - (Measured in Radian) - Direction of Motion of a Particle is angle which the projectile makes with the horizontal.
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.
Height - (Measured in Meter) - Height is the distance between the lowest and highest points of a person/ shape/ object standing upright.

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)
Height: 11.5 Meter --> 11.5 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

θ_pr = atan((sqrt((v_pm^2*(sin(α_pr))^2)-2*[g]*h))/(v_pm*cos(α_pr))) --> atan((sqrt((30.01^2*(sin(0.785223630472101))^2)-2*[g]*11.5))/(30.01*cos(0.785223630472101)))

Evaluating ... ...

θ_pr = 0.614810515101847

STEP 3: Convert Result to Output's Unit

0.614810515101847 Radian -->35.2260477156066 Degree (Check conversion here)

FINAL ANSWER

35.2260477156066 ≈ 35.22605 Degree <-- Direction of Motion of a Particle

(Calculation completed in 00.004 seconds)

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Institute of Aeronautical Engineering (IARE), Hyderabad

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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)

Direction of Projectile at given Height above Point of Projection Formula

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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 Direction of Projectile at given Height above Point of Projection?

Direction of Projectile at given Height above Point of Projection calculator uses 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))) to calculate the Direction of Motion of a Particle, Direction of Projectile at given Height above Point of Projection formula is defined as the angle of projection at a certain height above the point of projection, which determines the trajectory of a projectile under the influence of gravity, allowing us to predict the motion of objects in various fields such as physics and engineering. Direction of Motion of a Particle is denoted by θ_pr symbol.

How to calculate Direction of Projectile at given Height above Point of Projection using this online calculator? To use this online calculator for Direction of Projectile at given Height above Point of Projection, enter Initial Velocity of Projectile Motion (v_pm), Angle of Projection (α_pr) & Height (h) and hit the calculate button. Here is how the Direction of Projectile at given Height above Point of Projection calculation can be explained with given input values -> 2019.115 = atan((sqrt((30.01^2*(sin(0.785223630472101))^2)-2*[g]*11.5))/(30.01*cos(0.785223630472101))).

FAQ

What is Direction of Projectile at given Height above Point of Projection?

Direction of Projectile at given Height above Point of Projection formula is defined as the angle of projection at a certain height above the point of projection, which determines the trajectory of a projectile under the influence of gravity, allowing us to predict the motion of objects in various fields such as physics and engineering and is represented as θ_pr = atan((sqrt((v_pm^2*(sin(α_pr))^2)-2*[g]*h))/(v_pm*cos(α_pr))) or 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))). 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 & Height is the distance between the lowest and highest points of a person/ shape/ object standing upright.

How to calculate Direction of Projectile at given Height above Point of Projection?

Direction of Projectile at given Height above Point of Projection formula is defined as the angle of projection at a certain height above the point of projection, which determines the trajectory of a projectile under the influence of gravity, allowing us to predict the motion of objects in various fields such as physics and engineering is calculated using 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))). To calculate Direction of Projectile at given Height above Point of Projection, you need Initial Velocity of Projectile Motion (v_pm), Angle of Projection (α_pr) & Height (h). With our tool, you need to enter the respective value for Initial Velocity of Projectile Motion, Angle of Projection & Height and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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