# Projectile motion calculation

1. Mar 4, 2015

### Femme_physics

1. The problem statement, all variables and given/known data
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

3. The attempt at a solution

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

2. Mar 4, 2015

### 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.

3. Mar 4, 2015

### 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

4. Mar 4, 2015

### SammyS

Staff Emeritus
What is the arc-tangent of 10/8 ?

5. Mar 4, 2015

### Staff: Mentor

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...

6. Mar 4, 2015

### BvU

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

7. Mar 4, 2015

### Staff: Mentor

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.