Calculating Projectile Motion for Cannon and Window Scenario

[Femme_physics]

Homework Statement

A cannon has to fire a ball through a window in the wall. The window is 10 meters at the Y axis, and 8 meters (away from the cannon) at the X axis. The window is just slightly bigger than the ball (let's suppose that the dimensions are negligible). Find the required launching power.

Ball's mass: 0.6 kilograms
Angle of launch: 51.34 degrees

The Attempt at a Solution

I seem to be getting a strange initial velocity, way too high. Is my formula off? Or calculations?

 

[Suraj M]

Well,in your formula..,your $g$ should be $g= -9.8 units$.
Could you check your arithmetic again. And I hope you know how to do the rest of the question, though you have not posted it.

 

[BvU]

No, the lady is doing just fine. It takes a bit of sleuthing to track what you are doing, but it's correct.

Cannons can get huge muzzle speeds nowadays. It's not like they are throwing a stone or a ball...

However, a straight line to the window has slope 10/8 and atan(10/8) = 51.3402$^\circ$

And then the expression 10 - 8*tan gives zero !
In other words, muzzle speed has to be infinite.

That you get a finite result could well be due to rounding in the calculator.


Then: If the window is only slightly bigger than the cannonball, you'll have to lift the cannon 10 m up, or else the ball won't get through

 

[SammyS]

Homework Statement

A cannon has to fire a ball through a window in the wall. The window is 10 meters at the Y axis, and 8 meters (away from the cannon) at the X axis. The window is just slightly bigger than the ball (let's suppose that the dimensions are negligible). Find the required launching power.
http://s3.postimg.org/t777qpmhb/sketch.jpg

Ball's mass: 0.6 kilograms
Angle of launch: 51.34 degrees

The Attempt at a Solution

http://s4.postimg.org/hzhugcgd9/formula.jpg[/B]

I seem to be getting a strange initial velocity, way too high. Is my formula off? Or calculations?

What is the arc-tangent of 10/8 ?

 

[gneill]

There are any number of parabolic trajectories that can originate at the canon and reach the window. Given the tight fit, I suppose the trick is to choose one that happens to be traveling horizontally at the moment it passes though the window...

 

[BvU]

There are any number of parabolic trajectories that can originate at the canon and reach the window. Given the tight fit, I suppose the trick is to choose one that happens to be traveling horizontally at the moment it passes though the window...

So where does the given firing angle come from ? Femme or problem statement ?

 

[gneill]

So where does the given firing angle come from ? Femme or problem statement ?

It looks to be based upon the assumption of a straight-line trajectory from canon to window (not feasible with gravity acting). With a high enough initial velocity one could approach that goal if the window opening allows the ball to pass through at such an angle. Then it would be a matter of checking tolerances for such a scenario, but we don't have specifics.