Maximum Range of Flight for Inclined Projectile Solution

STEP 0: Pre-Calculation Summary
Formula Used
Range of Motion = (Initial Velocity^2*(1-sin(Angle of Plane)))/(Acceleration due to Gravity*(cos(Angle of Plane))^2)
Rmotion = (u^2*(1-sin(αpl)))/(g*(cos(αpl))^2)
This formula uses 2 Functions, 4 Variables
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)
Variables Used
Range of Motion - (Measured in Meter) - Range of Motion is defined as the total horizontal distance travelled by the object in a projectile motion.
Initial Velocity - (Measured in Meter per Second) - Initial Velocity is the velocity at which motion starts.
Angle of Plane - (Measured in Radian) - Angle of Plane denotes the angle made by the plain.
Acceleration due to Gravity - (Measured in Meter per Square Second) - Acceleration due to Gravity is acceleration gained by an object because of gravitational force.
STEP 1: Convert Input(s) to Base Unit
Initial Velocity: 35 Meter per Second --> 35 Meter per Second No Conversion Required
Angle of Plane: 0.7 Radian --> 0.7 Radian No Conversion Required
Acceleration due to Gravity: 9.8 Meter per Square Second --> 9.8 Meter per Square Second No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Rmotion = (u^2*(1-sin(αpl)))/(g*(cos(αpl))^2) --> (35^2*(1-sin(0.7)))/(9.8*(cos(0.7))^2)
Evaluating ... ...
Rmotion = 76.0239966825815
STEP 3: Convert Result to Output's Unit
76.0239966825815 Meter --> No Conversion Required
FINAL ANSWER
76.0239966825815 76.024 Meter <-- Range of Motion
(Calculation completed in 00.019 seconds)

Credits

Created by Mayank Tayal
National Institute of Technology (NIT), Durgapur
Mayank Tayal has created this Calculator and 25+ more calculators!
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National Institute Of Technology (NIT), Hamirpur
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3 Inclined Projectile Motion Calculators

Maximum Height Attained for Inclined Projectile
Go Maximum Height = ((Initial Velocity*sin(Angle of Inclination))^2)/(2*Acceleration due to Gravity*cos(Angle of Plane))
Maximum Range of Flight for Inclined Projectile
Go Range of Motion = (Initial Velocity^2*(1-sin(Angle of Plane)))/(Acceleration due to Gravity*(cos(Angle of Plane))^2)
Time of Flight for Inclined Projectile
Go Time of Flight = (2*Initial Velocity*sin(Angle of Inclination))/(Acceleration due to Gravity*cos(Angle of Plane))

Maximum Range of Flight for Inclined Projectile Formula

Range of Motion = (Initial Velocity^2*(1-sin(Angle of Plane)))/(Acceleration due to Gravity*(cos(Angle of Plane))^2)
Rmotion = (u^2*(1-sin(αpl)))/(g*(cos(αpl))^2)

What is Inclined Projectile Motion ?

Projectile motion on an inclined plane is one of the various projectile motion types. The main distinguishing aspect is that points of projection and return are not on the same horizontal plane. There are two possibilities : (i) the point of return is at a higher level than the point of projection i.e projectile is thrown up the incline and (ii) the Point of return is at a lower level than a point of projection i.e. projectile is thrown down the incline.

How to Calculate Maximum Range of Flight for Inclined Projectile?

Maximum Range of Flight for Inclined Projectile calculator uses Range of Motion = (Initial Velocity^2*(1-sin(Angle of Plane)))/(Acceleration due to Gravity*(cos(Angle of Plane))^2) to calculate the Range of Motion, The Maximum Range of Flight for Inclined Projectile formula is defined as the horizontal distance travelled by a projectile. Range of Motion is denoted by Rmotion symbol.

How to calculate Maximum Range of Flight for Inclined Projectile using this online calculator? To use this online calculator for Maximum Range of Flight for Inclined Projectile, enter Initial Velocity (u), Angle of Plane pl) & Acceleration due to Gravity (g) and hit the calculate button. Here is how the Maximum Range of Flight for Inclined Projectile calculation can be explained with given input values -> 76.024 = (35^2*(1-sin(0.7)))/(9.8*(cos(0.7))^2).

FAQ

What is Maximum Range of Flight for Inclined Projectile?
The Maximum Range of Flight for Inclined Projectile formula is defined as the horizontal distance travelled by a projectile and is represented as Rmotion = (u^2*(1-sin(αpl)))/(g*(cos(αpl))^2) or Range of Motion = (Initial Velocity^2*(1-sin(Angle of Plane)))/(Acceleration due to Gravity*(cos(Angle of Plane))^2). Initial Velocity is the velocity at which motion starts, Angle of Plane denotes the angle made by the plain & Acceleration due to Gravity is acceleration gained by an object because of gravitational force.
How to calculate Maximum Range of Flight for Inclined Projectile?
The Maximum Range of Flight for Inclined Projectile formula is defined as the horizontal distance travelled by a projectile is calculated using Range of Motion = (Initial Velocity^2*(1-sin(Angle of Plane)))/(Acceleration due to Gravity*(cos(Angle of Plane))^2). To calculate Maximum Range of Flight for Inclined Projectile, you need Initial Velocity (u), Angle of Plane pl) & Acceleration due to Gravity (g). With our tool, you need to enter the respective value for Initial Velocity, Angle of Plane & Acceleration due to Gravity 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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