Projectile Motion, missing variables.

[Visual1Up]

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

 

[rsk]

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?

 

[radou]

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

It's all about doing a little backwards thinking.

 

[Visual1Up]

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. . Excuse me if I am missing something, I am having a hard time with physics.

 

[rsk]

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

 

[Visual1Up]

oh, so are you saying... 0 = v sin 35 - (1/2)g * (4/(v sin 35))^2 ?

EDIT: v cos 35 on the right

 

[rsk]

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.

 

[Zeno's Paradox]

Visual1Up, I think you know how to derive the formula that gives range in function of $\theta , v_o$, which is:

$R = (v_0^2 \sin 2\theta)/g$

Then, it's easy.

 

[Visual1Up]

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 :(

 

[rsk]

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.

 

[Visual1Up]

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 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.