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Direction of Projectile at given Height above Point of Projection Formula

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Direction of Motion of a Particle is angle which the projectile makes with the horizontal. Check FAQs

θ pr = a \tan (\frac{\sqrt{({v pm}^{2} \cdot {(\sin (α pr))}^{2}) - 2 \cdot [g] \cdot h}}{v pm \cdot \cos (α pr)})

θ_pr - Direction of Motion of a Particle?v_pm - Initial Velocity of Projectile Motion?α_pr - Angle of Projection?h - Height?[g] - Gravitational acceleration on Earth?

Direction of Projectile at given Height above Point of Projection Example

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Here is how the Direction of Projectile at given Height above Point of Projection equation looks like with Values.

Here is how the Direction of Projectile at given Height above Point of Projection equation looks like with Units.

Here is how the Direction of Projectile at given Height above Point of Projection equation looks like.

35.226 = a \tan (\frac{\sqrt{({30.01}^{2} \cdot {(\sin (44.99))}^{2}) - 2 \cdot 9.8066 \cdot 11.5}}{30.01 \cdot \cos (44.99)})

35.226° = a \tan (\frac{\sqrt{({30.01m/s}^{2} \cdot {(\sin (44.99°))}^{2}) - 2 \cdot 9.8066m/s² \cdot 11.5m}}{30.01m/s \cdot \cos (44.99°)})

35.226 = a \tan (\frac{\sqrt{({30.01}^{2} \cdot {(\sin (44.99))}^{2}) - 2 \cdot 9.8066 \cdot 11.5}}{30.01 \cdot \cos (44.99)})

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Direction of Projectile at given Height above Point of Projection Solution

Follow our step by step solution on how to calculate Direction of Projectile at given Height above Point of Projection?

FIRST Step Consider the formula

θ pr = a \tan (\frac{\sqrt{({v pm}^{2} \cdot {(\sin (α pr))}^{2}) - 2 \cdot [g] \cdot h}}{v pm \cdot \cos (α pr)})

Next Step Substitute values of Variables

∴

θ pr = a \tan (\frac{\sqrt{({30.01m/s}^{2} \cdot {(\sin (44.99°))}^{2}) - 2 \cdot [g] \cdot 11.5m}}{30.01m/s \cdot \cos (44.99°)})

Next Step Substitute values of Constants

∴

θ pr = a \tan (\frac{\sqrt{({30.01m/s}^{2} \cdot {(\sin (44.99°))}^{2}) - 2 \cdot 9.8066m/s² \cdot 11.5m}}{30.01m/s \cdot \cos (44.99°)})

Next Step Convert Units

∴

θ pr = a \tan (\frac{\sqrt{({30.01m/s}^{2} \cdot {(\sin (0.7852rad))}^{2}) - 2 \cdot 9.8066m/s² \cdot 11.5m}}{30.01m/s \cdot \cos (0.7852rad)})

Next Step Prepare to Evaluate

∴

θ pr = a \tan (\frac{\sqrt{({30.01}^{2} \cdot {(\sin (0.7852))}^{2}) - 2 \cdot 9.8066 \cdot 11.5}}{30.01 \cdot \cos (0.7852)})

Next Step Evaluate

∴

θ pr = 0.614810515101847rad

Next Step Convert to Output's Unit

∴

θ pr = 35.2260477156066°

LAST Step Rounding Answer

∴

θ pr = 35.226°

Direction of Projectile at given Height above Point of Projection Formula Elements

Variables

Constants

Functions

Direction of Motion of a Particle

Direction of Motion of a Particle is angle which the projectile makes with the horizontal.

Symbol: θ_pr

Measurement: AngleUnit: °

Note: Value can be positive or negative.

Formulas to find Direction of Motion of a Particle

Initial Velocity of Projectile Motion

Initial Velocity of Projectile Motion is the velocity at which motion starts.

Symbol: v_pm

Measurement: SpeedUnit: m/s

Note: Value should be greater than 0.

Formulas to find Initial Velocity of Projectile Motion

Angle of Projection

Angle of Projection is angle made by the particle with horizontal when projected upwards with some initial velocity.

Symbol: α_pr

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Angle of Projection

Height

Height is the distance between the lowest and highest points of a person/ shape/ object standing upright.

Symbol: h

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Height

Gravitational acceleration on Earth

Gravitational acceleration on Earth means that the velocity of an object in free fall will increase by 9.8 m/s2 every second.

Symbol: [g]

Value: 9.80665 m/s²

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.

Syntax: sin(Angle)

cos

Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle.

Syntax: 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.

Syntax: 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.

Syntax: 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.

Syntax: sqrt(Number)

Other formulas in Projectile Motion category

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

v h = v pm \cdot \cos (α pr)

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

v v = v pm \cdot \sin (α pr)

Go Initial Velocity of Particle given Horizontal Component of Velocity

v pm = \frac{v h}{\cos (α pr)}

Go Initial Velocity of Particle given Vertical Component of Velocity

v pm = \frac{v v}{\sin (α pr)}

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

Direction of Projectile at given Height above Point of Projection evaluator 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 evaluate 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 evaluate Direction of Projectile at given Height above Point of Projection using this online evaluator? To use this online evaluator 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.

FAQs on Direction of Projectile at given Height above Point of Projection

What is the formula to find Direction of Projectile at given Height above Point of Projection?

The formula of Direction of Projectile at given Height above Point of Projection is expressed as 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))). Here is an example- 2019.115 = atan((sqrt((30.01^2*(sin(0.785223630472101))^2)-2*[g]*11.5))/(30.01*cos(0.785223630472101))).

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

With Initial Velocity of Projectile Motion (v_pm), Angle of Projection (α_pr) & Height (h) we can find Direction of Projectile at given Height above Point of Projection using the formula - 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))). This formula also uses Gravitational acceleration on Earth constant(s) and , Sine (sin), Cosine (cos), Tangent (tan), Inverse Tan (atan), Square Root (sqrt) function(s).

Can the Direction of Projectile at given Height above Point of Projection be negative?

Yes, the Direction of Projectile at given Height above Point of Projection, measured in Angle can be negative.

Which unit is used to measure Direction of Projectile at given Height above Point of Projection?

Direction of Projectile at given Height above Point of Projection is usually measured using the Degree[°] for Angle. Radian[°], Minute[°], Second[°] are the few other units in which Direction of Projectile at given Height above Point of Projection can be measured.

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Direction of Projectile at given Height above Point of Projection Formula

Direction of Projectile at given Height above Point of Projection Example

Direction of Projectile at given Height above Point of Projection Solution

Direction of Projectile at given Height above Point of Projection Formula Elements

Other formulas in Projectile Motion category

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

FAQs on Direction of Projectile at given Height above Point of Projection

Variable Name