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

In summary, the conversation discusses a trajectory problem where a ball is launched from ground level at an unknown angle and velocity. The ball travels 20 meters in the x direction and 25 meters up in the y direction before hitting a wall at a -45 degree angle. The goal is to find the initial velocity and speed when the ball hits the wall using given equations and information. The conversation also mentions the difficulty in finding the initial angle and the stress experienced in solving the problem. Possible hints include the parabolic path passing through points (0,0) and (20,25) and the gradient at (20,25) being -1.

## Homework Statement

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

## Homework 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

## 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

If the ball hits the wall at an angle of 45° after traveling 25m upwards, what does that tell you about what the maximum height reached would have been if the wall was not present?

Last edited:
Δ Y = Vo( Sin ∅o) - 1/2g (t)^2

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

## Homework Statement

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

## Homework 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

## 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

NascentOxygen said:
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.

217 MeV said:
If the ball hits the wall at an angle of 45° after traveling 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

"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?

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?

## 1. Why is the trajectory problem so difficult?

The trajectory problem can be challenging because it requires a thorough understanding of concepts such as velocity, acceleration, and projectile motion. It also involves complex mathematical calculations and may require the use of advanced equations and formulas.

## 2. What are some common mistakes when solving the trajectory problem?

Some common mistakes when solving the trajectory problem include not properly identifying and labeling all variables, using incorrect equations or formulas, and not considering all forces acting on the object. It is important to carefully follow the steps and double-check all calculations to avoid these errors.

## 3. Can you provide any tips for solving the trajectory problem?

One helpful tip for solving the trajectory problem is to break it down into smaller, more manageable steps. This can involve drawing diagrams, identifying known and unknown variables, and simplifying equations. Additionally, it is important to carefully read the problem and understand what it is asking for before attempting to solve it.

## 4. How can real-life applications of the trajectory problem be helpful?

The trajectory problem has many real-life applications, such as predicting the flight path of a baseball or calculating the trajectory of a rocket. These applications can help us understand and make predictions about the motion of objects in the world around us.

## 5. Are there any online resources that can help with solving the trajectory problem?

Yes, there are many online resources available that provide step-by-step guides and practice problems for solving the trajectory problem. Some examples include Khan Academy, Physics Classroom, and Brightstorm. It can also be helpful to consult with a tutor or classmate for additional support and guidance.

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