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)))
θpr = atan((sqrt((vpm^2*(sin(αpr))^2)-2*[g]*h))/(vpm*cos(αpr)))
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
θpr = atan((sqrt((vpm^2*(sin(αpr))^2)-2*[g]*h))/(vpm*cos(αpr))) --> atan((sqrt((30.01^2*(sin(0.785223630472101))^2)-2*[g]*11.5))/(30.01*cos(0.785223630472101)))
Evaluating ... ...
θpr = 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)

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 Vaibhav Malani
National Institute of Technology (NIT), Tiruchirapalli
Vaibhav Malani has verified this Calculator and 200+ more calculators!

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

Direction of Projectile at given Height above Point of Projection 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)))
θpr = atan((sqrt((vpm^2*(sin(αpr))^2)-2*[g]*h))/(vpm*cos(αpr)))

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, The Direction of projectile at given height above point of projection formula is defined as the ratio of vertical velocity at height attained to the horizontal component of velocity. Direction of Motion of a Particle is denoted by θpr 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 (vpm), Angle of Projection 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?
The Direction of projectile at given height above point of projection formula is defined as the ratio of vertical velocity at height attained to the horizontal component of velocity and is represented as θpr = atan((sqrt((vpm^2*(sin(αpr))^2)-2*[g]*h))/(vpm*cos(αpr))) 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?
The Direction of projectile at given height above point of projection formula is defined as the ratio of vertical velocity at height attained to the horizontal component of velocity 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 (vpm), Angle of Projection 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.
Let Others Know
Facebook
Twitter
Reddit
LinkedIn
Email
WhatsApp
Copied!