Kicking a Field Goal: Initial Speed Needed for Clear Crossbar

[NotVeryBright]

Homework Statement

If the ball is kicked at 53 degrees above horizontal what must the initial speed be if it is just to clear the crossbar. I know the ball is distance in the x direction is 10.98 m and the height of the goal post is 3.05 m.

Homework Equations

I think I should be using the equations Voy=Vosin(theta) and Vox=Vocos(theta)

The Attempt at a Solution

No idea how to solve without having any veclocities to plug into the above equations.

 

[berkeman]

Welcome to the PF. I moved your thread from Advanced Physics to Introductory Physics.

You have listed two of the equations that you will need to solve the problem. Now list the equation for motion x(t) in the horizontal direction, in terms of Vx(t) and Vox and t. And list the equation for motion in the vertical direction y(t), in terms of Vy(t) and Voy and t and the acceleration of gravity g.

With those equations of motion, and the ending (x,y) point you are given, do you see how you may not need to know the initial velocity Vo?

 

[baba89]

As a scientist, it is important to approach problems with a clear and systematic methodology. In this case, we are looking for the initial speed (V0) needed for a field goal to clear the crossbar, given the angle (53 degrees), distance in the x direction (10.98 m), and height of the goal post (3.05 m).

First, let's break down the problem into smaller components. We know that the motion of the ball can be described as a projectile, with an initial velocity (V0) and an angle (theta) above horizontal. We also know that the ball will follow a parabolic path, with a maximum height at its peak.

Using the equations provided, we can set up a system of equations to solve for V0. The equation for the vertical component of velocity (Voy) is Voy=V0sin(theta), and the equation for the horizontal component of velocity (Vox) is Vox=V0cos(theta).

Since we are looking for the initial speed needed for the ball to just clear the crossbar, we can set up a relationship between the height of the goal post and the maximum height of the ball. This can be done by using the equation for the maximum height of a projectile, which is hmax=Voy^2/2g, where g is the acceleration due to gravity.

We also know that the distance in the x direction (10.98 m) is equal to the horizontal component of velocity (Vox) multiplied by the time of flight (t). This can be represented as 10.98=V0cos(theta)*t.

Now, we have three equations with three unknowns (V0, theta, and t). We can use algebraic manipulation and substitution to solve for V0.

Once we have found the initial speed (V0), we can use it to calculate the time of flight (t) and the angle (theta) needed for the field goal to clear the crossbar. It is important to note that the initial speed needed may vary depending on the specific conditions, such as air resistance and the type of ball being used.

In conclusion, as a scientist, it is important to approach problems systematically and use mathematical equations to solve for unknown variables. In this case, we can use the equations for projectile motion and set up a relationship between the height of the goal post and the maximum height of the ball to solve for