Soccer goal. Need help defining height of ball at a distance.

[lorenzosounds]

Homework Statement

Write a program to determine whether or not a ball kicked is a goal. Initial distance (from goal), initial angle, and initial speed are user-defined variables. The net is 2.54 m high. Gravity is 9.81m/s^2

Homework Equations

flightTime=(2)initSpeed*sin(initAngle)/gravity

range=flightTime*initSpeed * cos(initAngle)

The Attempt at a Solution

Trying to define whether or not the ball is above the net when the ball is at the initial distance. I've been thinking about it in terms of trig functions, specifically Sin. Also, maybe using the pythagorean theorem (initDistance^2 + height of ball^2 = Length of tangent line between initDistance and ball^2).

I'm also aware of the kinematic equation vi^2 * (sinθi)^2/2g, which gives the max height of a parabolic flight. However, this doesn't let me define the height at any moment.

 

[lorenzosounds]

I found this formula defining height.

y(t) = (Vo sinm)) - (gt²)/2

What does the A-hat represent?

 

[Redbelly98]

Homework Statement

Write a program to determine whether or not a ball kicked is a goal. Initial distance (from goal), initial angle, and initial speed are user-defined variables. The net is 2.54 m high. Gravity is 9.81m/s^2

Homework Equations

flightTime=(2)initSpeed*sin(initAngle)/gravity

range=flightTime*initSpeed * cos(initAngle)

The Attempt at a Solution

Trying to define whether or not the ball is above the net when the ball is at the initial distance. I've been thinking about it in terms of trig functions, specifically Sin. Also, maybe using the pythagorean theorem (initDistance^2 + height of ball^2 = Length of tangent line between initDistance and ball^2).

I'm also aware of the kinematic equation vi^2 * (sinθi)^2/2g, which gives the max height of a parabolic flight. However, this doesn't let me define the height at any moment.

Welcome to Physics Forums.

"Relevant equations" should probably include all kinematic equations, applied to both horizontal and vertical motion.

You can use the kinematic equation that tells you the ball's height at any given time, given the acceleration and initial velocity.

Also, what is supposed to happen to the ball if it hits the ground before reaching the goal? Does it come to a complete stop, bounce off the ground, continue rolling along the ground, or something else?

 

[Redbelly98]

I found this formula defining height.

y(t) = (Vo sinm)) - (gt²)/2

What does the A-hat represent?

That looks similar to the following equation (2nd equation listed under "Displacement"):
http://en.wikipedia.org/wiki/Projectile_motion#Displacement

But there is no A-hat in that equation.

I'll suggest that you look at a physics textbook, in the section that discusses projectile motion, which will have all the equations and also explain what all the terms mean.

 

[Nickie]

As a scientist, it is important to have a clear understanding of the problem at hand before attempting to solve it. In this case, the problem is asking for a program that can determine whether a ball kicked towards a soccer goal is a goal or not. The program should take into account the initial distance from the goal, initial angle, and initial speed of the ball, as well as the height of the goal and the force of gravity.

To solve this problem, we can use the basic principles of projectile motion. In this case, the ball is being kicked at an angle, so we need to use both the horizontal and vertical components of the initial velocity. We can use the equations provided in the problem to calculate the flight time and range of the ball.

Once we have these values, we can use the vertical component of the initial velocity and the time to calculate the maximum height of the ball. This can be done using the kinematic equation, h = vi^2 * (sinθi)^2/2g. This will give us the maximum height of the ball at any given moment.

To determine if the ball is a goal or not, we need to compare the maximum height of the ball to the height of the goal. If the maximum height is greater than the height of the goal, then the ball is a goal. If it is lower, then it is not a goal.

In summary, to solve this problem, we need to use the equations provided to calculate the flight time and range of the ball, and then use the kinematic equation to calculate the maximum height of the ball at any given moment. We can then compare this height to the height of the goal to determine if the ball is a goal or not.