Solving Projectile Motion: Calculating Initial Velocity with Known Variables

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Homework Help Overview

The discussion revolves around calculating the initial velocity required for a projectile to travel a specified distance from a given height. The known variables include height, angle, distance traveled, acceleration due to gravity, and mass of the object, while the initial and final velocities and time are unknown.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants explore the relationships between the known variables and the equations of motion. Some express concerns about the applicability of certain equations due to the differing launch and landing heights, while others attempt to derive expressions for time and initial velocity based on the projectile motion equations.

Discussion Status

There is ongoing exploration of the problem, with participants questioning the validity of certain approaches given the height difference. Some have provided mathematical expressions to relate the variables, and there appears to be a productive exchange of ideas, though no consensus has been reached.

Contextual Notes

Participants note the challenge posed by the unknown time variable and the differing heights of launch and landing, which complicates the analysis.

Sundaze
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How can one go about calculating the initial velocity of an object needed to travel a certain distance, starting from atop a given height.

Variables known: height, angle, distance traveled, acceleration of gravity, mass of object
Not known: initial and final velocity, time
 
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Sundaze said:
How can one go about calculating the initial velocity of an object needed to travel a certain distance, starting from atop a given height.

Variables known: height, angle, distance traveled, acceleration of gravity, mass of object
Not known: initial and final velocity, time
Use the http://hyperphysics.phy-astr.gsu.edu/hbase/traj.html#tra4".

AM
 
Last edited by a moderator:
These do not work since the launch point is not at the same level as the landing. And time is unknoen.
 
Sundaze said:
These do not work since the launch point is not at the same level as the landing. And time is unknoen.

The range x = v*cosθ*t.

So t = x/v*cosθ

-y = v*sinθ*t - 0.5*g*t^2

-y = v*sinθ*x/v*cosθ - 0.5*g*(x/v*cosθ)^2

-y = x*tanθ - 0.5*g*x^2/v^2*cos^2(θ)

Now simplify and solve for v.
 
Sundaze said:
These do not work since the launch point is not at the same level as the landing. And time is unknoen.
If you scroll down on the link I gave you, you will see how to analyse the problem.

AM
 
rl.bhat said:
The range x = v*cosθ*t.

So t = x/v*cosθ

-y = v*sinθ*t - 0.5*g*t^2

-y = v*sinθ*x/v*cosθ - 0.5*g*(x/v*cosθ)^2

-y = x*tanθ - 0.5*g*x^2/v^2*cos^2(θ)

Now simplify and solve for v.

Thanks, it all makes sense now.
 

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