Projectile Motion, missing variables.

  • Thread starter Visual1Up
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  • #1
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I am having some trouble with projectile motion, I do fine when I have all of the variables such as initial velocity, and angle, and say I want to find the range. That's great, I use y = voyt - 1/2 gt^2 where y = 0 to find the time, since voy = vo sin theta, and r = voxt where vox = vo cos theta. But I am having trouble when problems are taking the velocity or angle away.

Such as...theta is 35, range is 4m, find the initial velocity... something along those lines. I get horribly stuck because now I "can't" find voy, or vox, etc. Would anyone mind helping? Thanks!,

-Mike :bugeye:
 

Answers and Replies

  • #2
rsk
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174
You'd tackle this one by first considering horizontal motion. You don't know Vo but you kwo the relationship between Vo, theta and t because you have the distance.

So you have an expression for t in terms of v (t = 4/vcos35)

Then you look at the vertical remembering that when the stone has landed, the vertical displacemetn is zero

y = voyt - 1/2 gt^2 using the expression you have for t.

You end up with v as the only variable.

Does that help?
 
  • #3
radou
Homework Helper
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Visual1Up said:
Such as...theta is 35, range is 4m, find the initial velocity... something along those lines. I get horribly stuck because now I "can't" find voy, or vox, etc. Would anyone mind helping? Thanks!,

-Mike :bugeye:

It's all about doing a little backwards thinking. :smile:
 
  • #4
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rsk said:
You'd tackle this one by first considering horizontal motion. You don't know Vo but you kwo the relationship between Vo, theta and t because you have the distance.

So you have an expression for t in terms of v (t = 4/vcos35)

Then you look at the vertical remembering that when the stone has landed, the vertical displacemetn is zero

y = voyt - 1/2 gt^2 using the expression you have for t.

You end up with v as the only variable.

Does that help?

I think I understand, your saying the equation turns into y = 1/2gt^2? since voy = 0. but when working that I get 42 m/s and t = .1 . That can't be right. :uhh: . Excuse me if I am missing something, I am having a hard time with physics.
 
  • #5
rsk
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Visual1Up said:
I think I understand, your saying the equation turns into y = 1/2gt^2? since voy = 0.

No - it has vertical velocity. But when it lands it has no vertical displacement, so y = 0, not Voy

Voy = Vo sin theta
 
  • #6
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oh, so are you saying... 0 = v sin 35 - (1/2)g * (4/(v sin 35))^2 ???

EDIT: v cos 35 on the right
 
  • #7
rsk
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0 = Vosin35 t - 1/2 g t^2

0 = Vosin35 4/cos35 - 1/2 g (4/Vocos35)^2

I think you missed the t from the first part.
 
  • #8
Visual1Up, I think you know how to derive the formula that gives range in function of [itex]\theta , v_o[/itex], which is:

[itex]R = (v_0^2 \sin 2\theta)/g[/itex]

Then, it's easy. :smile:
 
  • #9
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Well with rsk's problem, I can't ever arrive at the right answer because the math is killing me. I have never seen zeno's problem before but when working I get vo = .649 and time = 7.5 sec which can't be right. I am horrible at this :(
 
  • #10
rsk
258
174
Ok, go from here

0 = Vosin35 t - 1/2 g t^2

and let's cancel a t from each part before we start.....

0 = Vosin35 - 1/2 g t

Subs in for t, from before

0 = Vosin35 - 1/2 g (4/Vocos35)

Or in other words


Vosin35 = 1/2 g (4/Vocos35)

Rearranging gives

Vo^2 = 1/2 g 4 /(sin35 cos35)



Work out your sines and cosines and you should get a value of 6.46 for Vo

I've worked it backwards to find t, and to check the x and y displacements, and it works.
 
  • #11
12
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rsk said:
Ok, go from here

0 = Vosin35 t - 1/2 g t^2

and let's cancel a t from each part before we start.....

0 = Vosin35 - 1/2 g t

Subs in for t, from before

0 = Vosin35 - 1/2 g (4/Vocos35)

Or in other words


Vosin35 = 1/2 g (4/Vocos35)

Rearranging gives

Vo^2 = 1/2 g 4 /(sin35 cos35)



Work out your sines and cosines and you should get a value of 6.46 for Vo

I've worked it backwards to find t, and to check the x and y displacements, and it works.

ahhhh I forgot to factor out a t :frown: ok I got 6.46. It seems like the math does me in more than the formula's. But thank you very much for the help.
 

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