Max Field Goal Distance for Vo=68, k=.027, theta=39 Degrees

In summary, the conversation discusses the conditions for a successful field goal in American football, where the ball must pass between the uprights and over the crossbar. The maximum distance for a field goal without considering drag forces is 126.64 in the horizontal direction. The following question involves deriving equations for the horizontal and vertical positions of the ball as functions of time, considering a crude model for drag force. However, the speaker is unsure how to approach this problem and is seeking help from others.
  • #1
2slowtogofast
135
1
When Vo=68 ; k=.027 ; theta = 39 degrees

(a) The American Football kicker lines up to attempt a field goal . Take the balls initial position to be the origin. For the field goal to be good it must pass between the upstairs, and over the crossbar which are 10 feet above ground level. Assuming the ball is kicked straight ( directly between the upright ), and the ball is given an initial velocity of Vo at an angle theta answer the following questions.

(a)What is the maximum field goal distance for this kicker if you ignore all drag forces.

I solved (a) to be 126.64 in the x direction.

(b) If we include a crude model for the drag force in which the net acceleration on the ball is given by:
a=(-k * vx ) i + (-g -k * Vy) j ( ft/s2 )

Derive the equations describing the horizontal and vertical positions as functions of time.- I am lost when I get to (b) and also i couldt get the picture to load but its basicly a football x yards away from a goal post 10 ft in the air. I am just confused on how to start this off my teacher said there would be a few integrals in this problem and i tried relating

a = dv/dt solving for v then v = ds/dt for each component but it didt work

the vx and vy are velocity in x nd veloctiy in y i just couldt get the subscipts on this computer I am on
 
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  • #2
anybody have any ideas
 
  • #3
2slowtogofast: Perhaps try thread 291331.
 

FAQ: Max Field Goal Distance for Vo=68, k=.027, theta=39 Degrees

What is the equation for calculating the maximum field goal distance?

The equation for calculating the maximum field goal distance is d = (v02 * sin(2θ))/g, where d is the maximum distance, v0 is the initial velocity, θ is the launch angle, and g is the acceleration due to gravity.

What are the values for Vo, k, and theta in the given equation?

The values for Vo, k, and theta in the given equation are Vo=68, k=.027, and theta=39 degrees.

How do Vo, k, and theta affect the maximum field goal distance?

Vo, k, and theta all play a role in determining the maximum field goal distance. A higher initial velocity (Vo) will result in a longer distance, while a lower initial velocity will result in a shorter distance. The drag coefficient (k) and launch angle (theta) also affect the distance, with a lower drag coefficient and a higher launch angle resulting in a longer distance.

What is the significance of the given values for Vo, k, and theta?

The given values for Vo, k, and theta represent the initial conditions of the field goal kick. These values can be adjusted to determine the maximum distance that the ball can travel under different circumstances, such as a different initial velocity or launch angle.

How can the maximum field goal distance be increased?

The maximum field goal distance can be increased by increasing the initial velocity, reducing the drag coefficient, or increasing the launch angle. Additionally, factors such as wind speed and direction can also affect the maximum distance.

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