How to Calculate the Initial Speed Required for a Field Goal Kick?

Question:

What is the initial speed v needed for a placekicker to kick a field goal that just clears the 2.75 m high crossbar?

Answer:

The initial speed v required for a placekicker to kick a field goal can be calculated using the equations of projectile motion. Given the vertical and horizontal displacements, as well as the angle of the kick, we can solve for the required initial speed. This type of problem is commonly encountered at the High School level in physics.

Explanation:

Projectile Motion Equations:
The problem you're trying to solve involves projectile motion, a fundamental concept in physics. To find the initial speed v at which the ball must be kicked, we can use the following equations:

y = x*tan(θ) - [g*x^2] / [2*v^2*cos^2(θ)]
x = v*cos(θ)*t
y = v*sin(θ)*t - 0.5*g*t^2

In this specific scenario, the values are x = 27.0 m, y = 2.75 m, and θ = 35.0°. By substituting these values into the equations and solving for v, we can determine the initial speed required for the kick to clear the crossbar successfully.

Projectile motion problems like this one are a great way to apply physics concepts and understand how forces and angles affect the motion of an object in the air. By mastering these calculations, you can improve your understanding of physics principles and their real-world applications.