Solving Projectile Motion: Calculating Initial Velocity with Known Variables

[Sundaze]

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

 

[Andrew Mason]

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

 

[Sundaze]

These do not work since the launch point is not at the same level as the landing. And time is unknoen.

 

[rl.bhat]

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.

 

[Andrew Mason]

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

 

[Sundaze]

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.