Vertical / Horizontal Displacements

In summary, the conversation is about a person seeking help with their math skills in preparation for an upcoming degree. They are struggling with a specific question involving a ball's trajectory and are looking for guidance. The question involves finding the maximum vertical displacement of the ball and determining if it will go over a wall. The person also mentions having more questions but wanting to solve them on their own once they understand the first one. They apologize for the lengthy explanation and express their lack of confidence in math.
  • #1
JJKD
1
0
Hey guys! Firstly, let me start by apologizing if this is completely the wrong place to put this question. As you'll soon tell my maths is... well, questionable at best.

Let me just give some context to avoid any assumptions :) I'm starting an OU degree in autumn with my first module being mathematics. My maths knowledge didn't get any further than high school so it's a bit of a challenge. I've been trying to revise using practise papers and bring myself at least up to scratch but this is proving difficult. There are some questions where I'm spending hours on them which would take some of you 10 minutes. But this question here is driving me nuts...

The question:

A boy standing on a level playing field kicks a ball into the air from the
ground at his feet. The trajectory of the ball can be modeled by the
equation

y=3x - x^2/2

where x is the horizontal displacement (in metres) of the ball from the
boy and y is the vertical displacement (in metres) measured from the
ground.

(i) Find the maximum vertical displacement of the ball.

(ii) If there is a 3 metre high wall at a distance of 5 metres from the
boy, in the direction the ball is travelling, will the ball be kicked
over the wall? Explain your answer.​

I have lots more questions like this but I want to work those out myself when I have an understanding of the first one :/

Sorry this is a pretty big 'text dump', but my math ability is pretty bad and I don't even know where to begin.

Cheers guys!
Jay
 
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  • #2
(i) What does the $y$-coordinate of the vertex of the parabola represent?

(ii) What is the value of $y$ when $x$ is 5?
 

1. What is the difference between vertical and horizontal displacements?

Vertical displacement refers to the change in height or elevation of an object, while horizontal displacement refers to the change in position or distance along the horizontal axis. In other words, vertical displacement moves an object up or down, while horizontal displacement moves it left or right.

2. How are vertical and horizontal displacements measured?

Vertical and horizontal displacements are typically measured using a coordinate system, such as the Cartesian coordinate system. Vertical displacement is measured along the y-axis, while horizontal displacement is measured along the x-axis. The units of measurement can vary, but are often in meters or feet.

3. What factors can cause vertical and horizontal displacements?

Vertical and horizontal displacements can be caused by a variety of factors, including force, motion, and external influences such as gravity, wind, or tectonic plate movement. These displacements can also be intentional, such as in construction projects or transportation systems.

4. How do vertical and horizontal displacements affect structures?

Vertical and horizontal displacements can have significant effects on structures. Vertical displacements can cause changes in stress and strain, leading to potential structural failure or damage. Horizontal displacements can also create stress and strain, and can cause structures to shift or collapse. Careful consideration and engineering are necessary to ensure the stability of structures in the face of displacements.

5. How are vertical and horizontal displacements used in scientific research?

Vertical and horizontal displacements are important to understand and measure in many fields of science, including geology, physics, and engineering. They can provide valuable information about the properties and behavior of materials and structures, and can aid in predicting and preventing natural disasters such as earthquakes and landslides.

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