Kicking a Field Goal: Calculating Elevation Angles

In summary, the maximum and minimum elevation angles for a football kicker to score a field goal from a point 48 m in front of goalposts with a horizontal bar 3.44 m above the ground are determined by using standard constant acceleration equations for the x and y directions to find a relationship between the angle and the tangent of the angle.
  • #1
sagaradeath
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Homework Statement



A football kicker can give the ball an initial speed of 30 m/s. What are the (a) least and (b) greatest elevation angles at which he can kick the ball to score a field goal from a point 48 m in front of goalposts whose horizontal bar is 3.44 m above the ground?

Homework Equations





The Attempt at a Solution


 
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  • #2
hi sagaradeath! :wink:

show us what you've tried, and where you're stuck, and then we'll know how to help! :smile:
 
  • #3
thatz the thing i don't know how to start it
 
  • #4
call the angle θ, and use standard constant acceleration equations for the x and y directions (separately)
 
  • #5


I would first gather all the necessary information and clarify any uncertainties in the problem. From the given information, it can be assumed that the ball is kicked from a point 48 m away from the goalposts, and the horizontal bar of the goalposts is 3.44 m above the ground. The initial speed of the ball is given as 30 m/s.

To calculate the elevation angles, we can use the equation:

θ = arctan (h/x)

Where θ is the elevation angle, h is the height of the goalposts (3.44 m), and x is the horizontal distance between the point of kick and the goalposts (48 m).

(a) To find the least elevation angle, we can rearrange the equation to solve for θ:

θ = arctan (h/x)

θ = arctan (3.44/48)

θ = 4.09°

Therefore, the least elevation angle at which the ball can be kicked to score a field goal is approximately 4.09°.

(b) To find the greatest elevation angle, we can use the same equation and substitute the initial speed of the ball (30 m/s) for x:

θ = arctan (h/x)

θ = arctan (3.44/30)

θ = 6.60°

Therefore, the greatest elevation angle at which the ball can be kicked to score a field goal is approximately 6.60°.

It is important to note that these calculations are based on ideal conditions and do not take into account external factors such as air resistance, wind, and the trajectory of the ball. In reality, the elevation angles may vary slightly due to these factors. Additionally, the skill and technique of the kicker can also affect the outcome.
 

FAQ: Kicking a Field Goal: Calculating Elevation Angles

1. What is the purpose of calculating elevation angles when kicking a field goal?

The purpose of calculating elevation angles is to determine the optimal trajectory for the football in order to successfully kick a field goal. This involves calculating the correct angle at which the ball should be kicked, taking into account factors such as distance, wind speed and direction, and the height of the goal posts.

2. What factors are involved in calculating elevation angles for a field goal?

There are several factors that must be taken into account when calculating elevation angles for a field goal. These include the distance from the ball to the goal posts, the height of the goal posts, wind speed and direction, and the weight and shape of the football.

3. How does wind speed and direction affect the calculation of elevation angles for a field goal?

Wind speed and direction play a significant role in determining the optimal elevation angle for a field goal. A strong headwind will require a lower angle to compensate for the added resistance, while a tailwind will require a higher angle to take advantage of the extra push. Crosswinds can also affect the trajectory of the ball, requiring adjustments to the angle.

4. Can you calculate elevation angles for a field goal without using mathematical equations?

While it is possible to estimate the elevation angle for a field goal based on experience and trial and error, using mathematical equations provides a more accurate calculation. Factors such as wind speed and direction, as well as the weight and shape of the football, can vary and greatly impact the trajectory of the ball.

5. Is there a specific elevation angle that will guarantee a successful field goal?

No, there is not a single elevation angle that will guarantee a successful field goal. The optimal angle will vary depending on the specific circumstances of each kick, such as distance, wind conditions, and the skill of the kicker. However, by accurately calculating the elevation angle, the chances of a successful field goal can be greatly increased.

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