Solving Projectile Motion: Calculating Initial Velocity with Known Variables

AI Thread Summary
To calculate the initial velocity of an object launched from a height to cover a specific distance, one must consider the known variables: height, angle, distance traveled, acceleration due to gravity, and mass. The equations of projectile motion can be adapted to account for the height difference, leading to a relationship involving time, which remains unknown. The range equation x = v*cosθ*t can be manipulated to express time in terms of velocity and distance. By substituting this expression into the vertical motion equation, one can derive a formula to solve for the initial velocity. Understanding these relationships clarifies the calculation process for projectile motion involving different launch and landing heights.
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
 
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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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