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The only trajectory problem on my whole SI sheet (trajectory) I cannot do!

by realfuzzhead
Tags: sheet, trajectory
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realfuzzhead
#1
Mar10-12, 01:47 AM
P: 14
1. The problem statement, all variables and given/known data
This a trajectory problem. A ball is launched from ground level at a unknown angle. ( ∅o= ? ) at an unknown velocity ( Vo = ? )

The ball travels 20 meters in the x direction and 25 meters up in the y direction. At this point (20,25) the ball hits a wall and a -45 angle below the horizon. Find the initial velocity ( Mag and direction ) and the speed when the ball hits the wall

2. Relevant equations

the only equations we have been given are

Vyfinal = Vo( Sin ∅o) - gt
Δ Y = Vo( Sin ∅o) - 1/2g (t)^2

ΔX = Vo(cos ∅) (t)

Vo( Cos ∅o) = Vf(Cos ∅o)

Xmax = (Vo^2 * (Sin 2∅))/ g


3. The attempt at a solution

I cannot post all my notes. I have finished, and double checked all my other answers on 2 whole trajectory work sheets. But I cannot for the life of me figure out how to find the initial angle as a function of the final angle again the change in distance.
I have even tried switching the whole problem around and shooting at 45 from 25 meters up and I still cannot find a result that works.

I have done probably 10-11 different tries of canceling out different variables (especially Vo and Vf and T) and finding them as products or sums of other variables, but I can never find a way to get the original y velocity or the orignal x velocity.

I do know that when the ball hits the wall the Y velocity is = to the -(x velocity), because tan-1 45 = -1 (-y/x)

I have spent over 2 hours on this problem and I have searched the interwbs for help but I cannot for the life of me figure out how to find the original angle if I know the final angle but don't know either the final or intial x or y velocities. I also don't know the time

I really, really don't like asking for answers to problems because I really like sitting down with a cup of joe and figuring it out for myself and actually learning, but I literally have grown some grey hairs and ruined my weekend over the amount of stress I have experienced over this problem, and I would really really appreciate if someone could answer this one if not give me a HUGE hint
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217 MeV
#2
Mar10-12, 04:47 AM
P: 25
If the ball hits the wall at an angle of 45 after travelling 25m upwards, what does that tell you about what the maximum height reached would have been if the wall was not present?
NascentOxygen
#3
Mar10-12, 04:54 AM
HW Helper
Thanks
P: 5,166
Δ Y = Vo( Sin ∅o) - 1/2g (t)^2
Should be Δ Y = Vo( Sin ∅o)t - 1/2g (t)^2

PeterO
#4
Mar10-12, 05:46 AM
HW Helper
P: 2,316
The only trajectory problem on my whole SI sheet (trajectory) I cannot do!

Quote Quote by realfuzzhead View Post
1. The problem statement, all variables and given/known data
This a trajectory problem. A ball is launched from ground level at a unknown angle. ( ∅o= ? ) at an unknown velocity ( Vo = ? )

The ball travels 20 meters in the x direction and 25 meters up in the y direction. At this point (20,25) the ball hits a wall and a -45 angle below the horizon. Find the initial velocity ( Mag and direction ) and the speed when the ball hits the wall

2. Relevant equations

the only equations we have been given are

Vyfinal = Vo( Sin ∅o) - gt
Δ Y = Vo( Sin ∅o) - 1/2g (t)^2

ΔX = Vo(cos ∅) (t)

Vo( Cos ∅o) = Vf(Cos ∅o)

Xmax = (Vo^2 * (Sin 2∅))/ g


3. The attempt at a solution

I cannot post all my notes. I have finished, and double checked all my other answers on 2 whole trajectory work sheets. But I cannot for the life of me figure out how to find the initial angle as a function of the final angle again the change in distance.
I have even tried switching the whole problem around and shooting at 45 from 25 meters up and I still cannot find a result that works.

I have done probably 10-11 different tries of canceling out different variables (especially Vo and Vf and T) and finding them as products or sums of other variables, but I can never find a way to get the original y velocity or the orignal x velocity.

I do know that when the ball hits the wall the Y velocity is = to the -(x velocity), because tan-1 45 = -1 (-y/x)

I have spent over 2 hours on this problem and I have searched the interwbs for help but I cannot for the life of me figure out how to find the original angle if I know the final angle but don't know either the final or intial x or y velocities. I also don't know the time

I really, really don't like asking for answers to problems because I really like sitting down with a cup of joe and figuring it out for myself and actually learning, but I literally have grown some grey hairs and ruined my weekend over the amount of stress I have experienced over this problem, and I would really really appreciate if someone could answer this one if not give me a HUGE hint
The parabolic path followed passes through 0,0 and 20,25, and the gradient at (20,25) is -1
The second derivative anywhere is -9.8

Surely if you put all that together the answer can be extracted
That enables you
realfuzzhead
#5
Mar10-12, 02:18 PM
P: 14
Quote Quote by NascentOxygen View Post
Should be Δ Y = Vo( Sin ∅o)t - 1/2g (t)^2
I typed this very late last night, I promise you that that "t" was there in every single one of my equations. I lose track of variables when I have to keep typing out all the little subscripts and figures, sorry.

Quote Quote by 217 MeV View Post
If the ball hits the wall at an angle of 45 after travelling 25m upwards, what does that tell you about what the maximum height reached would have been if the wall was not present?
it hits the wall at a -45 degree angle after it maximum y value
realfuzzhead
#6
Mar10-12, 02:20 PM
P: 14
"The parabolic path followed passes through 0,0 and 20,25, and the gradient at (20,25) is -1
The second derivative anywhere is -9.8

Surely if you put all that together the answer can be extracted
That enables you"


I just started calculus 2 weeks ago. I am decent with derivatives but to be honest I have never done a lick of integration, which is what I would need to go from having the derivative to the original right?
cmb
#7
Mar10-12, 03:27 PM
P: 628
Define a time, t, for yourself, that being how long it takes to get to the wall. So we know at time t its horizontal and vertical velocities are both 20/t.

Now ask a different question - with initial velocities 20/t both horiz and vertical, from a height 25, what angle will its flight intersect the horizontal if it goes from there?


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