Calculating Human Cannonball Flight Time with Given Velocity and Distance

[STrain]

Homework Statement

Emanuel Zacchini, the famous human cannonball of the Ringling Bros. and Barnum & Bailey Circus, was fired out of a cannon with a speed of 24.0 m/s. at an angle of 40.0o to the horizontal. If he landed in a net 56.6 m away at the same height from which he was fired, how long was Zacchini in the air?

Homework Equations

vr = 24.0 m/s
q = 40.0o
dx = 56.6 m
ay= 9.8 m/s2
I know that I need to use find Vx and use it to find Dx but I am not good at these types of problems, thanks in advance.

 

[fss]

Draw a picture. To find v_x, what trigonometric function would you use just based on the geometry of the problem?

 

[STrain]

I have drawn a picture but not sure what to do after that. I have the base and the angle labeled but I am not sure what trig function to use.

 

[fss]

I have drawn a picture but not sure what to do after that. I have the base and the angle labeled but I am not sure what trig function to use.

You have an angle, the hypotenuse, and are looking for the adjacent side.

 

[STrain]

I do not understand where I would be getting the hypotenuse from. I thought that I already had the adjacent side which would be 28.3 because that is half of the distance he was shot, and then the angle of 40 degrees.

 

[fss]

I do not understand where I would be getting the hypotenuse from. I thought that I already had the adjacent side which would be 28.3 because that is half of the distance he was shot, and then the angle of 40 degrees.

No, you are talking about the displacement vector, I am talking about the velocity vector. Re-draw (or re-label) your picture in which you have the velocity vector of magnitude 24.0 m/s at an angle of 40 degrees above the horizontal. Find the horizontal component of this vector using the given information.

Since you know that v_x and v_y don't depend on each other, to find the time of flight just use d_x = v_xt.

 

[STrain]

Ok, I think I understand now, I think then that the answer is 3.07 seconds. I found this by taking 24*cos(40) and dividing 56.6 by that.

 

[MysticDude]

I don't want to confuse you anymore(as I haven't done the problem myself), but can't you do this problem using the $$y-y_0 = v_0sin(\theta)t-\frac{1}{2}gt^{2}$$ and do some algebra to isolate t and get the answer? I mean since the guy's height at the end was the same as the initial(displacement), we'll have $$0 = 24sin(40)t - 4.9t^{2}$$. Can anyone verify this?

 

[Dick]

Ok, I think I understand now, I think then that the answer is 3.07 seconds. I found this by taking 24*cos(40) and dividing 56.6 by that.

Yes, I think you've got it. The x velocity is constant.