Dynamics problem involving projectile kinematics

[Khamul]

Homework Statement

Three children are throwing snowballs at each other. Child A throws a snowball with a horizontal velocity, V₀. If the snowball just passes over the head of child B and hits child C, determine (a) value of V₀, (b) distance d.

Homework Equations

V₀= V_0,x + V_0,y
V_0,x=V_i*cos($$\theta$$)
V_0,y=V_i*sin($$\theta$$)
x=x₀+v*t
v=v₀+a*t
x=x₀+v₀*t+[(1/2)*a*t²]
v²=v₀²+2*a(x-x₀)

The Attempt at a Solution

Thus far I am beating my head against the wall in the very beginning. I feel like I am missing something here; I feel like if I had been given the initial velocity I would be having a much easier time solving anything else. I know that the vertical acceleration is a constant -9.81 m/s², but I am unsure of the horizontal components' acceleration, seeing as how I do not know the final distance, the time, or the initial velocity. (and in my case, the acceleration for the horizontal component as well.) Also if it helps, I'm setting the child point A as my origin.

I know I'm missing something here...could anyone take pity on me and help end my three hour-long blight of face-to-desk'ing? Thank you!

4. F.B.D.
Unfortunately, I do not have a diagram with me...however the post this fellow made over at Cramster is a crude representation. From Child A to B, there is a vertical distance of 1 m, and a horizontal distance of 7m; and from child B to C, there is a vertical distance of 2 m, and a horizontal distance "d".

http://www.cramster.com/answers-jan-10/mechanical-engineering/kinematics-particles-1198-children-throwing-snowballs_750535.aspx

 

[tiny-tim]

Welcome to PF!

Hi Khamul! Welcome to PF!

… I am unsure of the horizontal components' acceleration, seeing as how I do not know the final distance, the time, or the initial velocity. (and in my case, the acceleration for the horizontal component as well.)

The horizontal acceleration is zero (why would it be anything else? ) …

x = v₀t

 

[Khamul]

Hello tiny-tim, and thank you for the greeting! :)

Ah, and would it be zero? I figured since it has a change in the velocity, (the initial is equal to something, and the final is 0) than it must have some acceleration. I see I was wrong though! Would this also mean that the initial velocity in the vertical direction is zero?

And sort of following up on that, that still leaves me with the dilemma of not being given time. Could the time be found rearranging v=v0+a*t for the vertical component, since we know the acceleration is gravity? (this of course assuming that the answer to my above answer about the vertical direction being yes.)

Thanks again for the help!

 

[L2E]

Hi Khamul, you have to realize that in these projectile motion questions, you are looking at the path of the projectile when it is freely moving through the air (generally assumed vacuum to be more accurate). therefore, the analysis of the projectile is from the moment it leaves one child's hand till the moment it hits the other child because it hits the other child at a velocity, that is the final velocity. This is why there is no horizontal acceleration it is the same at the start and end.

The initial velocity in the vertical direction is something, if the snowball is thrown at an angle of 0 degrees, the initial vertical velocity will be 0. because your question only mentions that the snowball is thrown with a horizontal velocity, it would probably be safe to assume that there is no vertical velocity if no initial angle is given.

to solve your problem, you need to use more than one equation and solve simultaneously.

 

[tiny-tim]

Hi Khamul!

(just got up :zzz: …)

Yes, the horizontal acceleration of a projectile is always zero.

This is because of good ol' Newton's second law (as nearly everything in dynamics is!) …

acceleration = force/mass (F = ma), and in this case the only force is gravity which is purely vertical, so the acceleration is also purely vertical!

(and since the question says that the child "throws a snowball with a horizontal velocity, V₀", yes, that means that the initial velocity in the vertical direction is zero)

and now (as usual with projectile problems) you need to write two standard constant acceleration equations for the x and y directions (separately), with a = 0 and -g of course, and solve them for t (as L2E says)

 

[Khamul]

Hi Khamul!

(just got up :zzz: …)

Yes, the horizontal acceleration of a projectile is always zero.

This is because of good ol' Newton's second law (as nearly everything in dynamics is!) …

acceleration = force/mass (F = ma), and in this case the only force is gravity which is purely vertical, so the acceleration is also purely vertical!

(and since the question says that the child "throws a snowball with a horizontal velocity, V₀", yes, that means that the initial velocity in the vertical direction is zero)

and now (as usual with projectile problems) you need to write two standard constant acceleration equations for the x and y directions (separately), with a = 0 and -g of course, and solve them for t (as L2E says)

As did I! Certainly been kept busy, hehe. :tongue:
Ahh, I see! That makes much more sense, and makes it solvable...I hope .

Thank you tiny-tim and L2E both for your input very much! Hope you don't mind if I bump again if I run into any more questions!

 

[Khamul]

Woohoo! Right (I was actually typing to ask another question) as I was about to ask for some help, I solved the puzzle!

I was about to ask, "well I STILL don't know the final x distance covered..) But I DO know the x distance, AND y distance covered to child B..and since the initial and final horizontal velocities are the same, (no acceleration in the horizontal), I can just use that information. Thanks for the help!


(Stay tuned for another incoming question, I'm sure!)