Solving a Football Kicking Problem with PreCalc

  • Thread starter mandomansion
  • Start date
  • Tags
    Precalc
In summary, the problem involves Scott kicking a football with an initial velocity of 50 ft/sec at an angle of 65 degrees with the horizontal and at a height of 3 feet. The equations that would model this situation are: x(t) = (50 * cos 65)t and y(t) = -16.1t^2 + (50 * sin 65)t + 3. The maximum height of the ball is 107.694 feet, it lands 190.178 feet away from Scott, and it is in the air for approximately 4.3 seconds. To solve this problem on a TI-83 calculator, the mode settings should be in degrees and the acceleration should be set to 32 feet/s
  • #1
mandomansion
5
0
Scott kicked a football with an initial velocity of 50 ft/sec at an angle of 65 degrees with the horizontal and at a height of 3 feet. Write the equations that would model this situation and answer the following:

a)
x(t) = _____________ (fill in formula with variable values plugged in)
y(t) = _____________ (fill in formula with variable values plugged in)

b) What is the max height of the ball?
c) How far did the ball land from Scott?
d) How long was the ball in the air?


Calculator problem if that wasn't obvious enough.




Formulas:

x(t) = (V * cos x)t
y(t) = -0.5gt^2 + (V * sin x)t + h




My attempts: (which are wrong by the way)

a)
x(t) = (50 * cos 65)t [CORRECT]
y(t) = -0.5(9.8)t^2 + (50 * sin 65)t + 3 [ITALICIZED PART IS WRONG; I figured g stood for gravity, so 9.8, right?]

b)
107.694 ft (didn't get formula right, and probably didn't use calculator correctly, so these are probably far off)

c)
190.178 ft.

d)
Didn't have enough time to finish.





This is a pretty quick PreCalc problem if you know what you're doing (which I didn't), so it would really help if one could do this.

And if one could tell me what mode settings my TI-83 should be on when I do this, I'd appreciate it.

And I apologize; in my 1AM rush to figure this problem out so I don't get another 10 points off on another test, I posted this in the wrong forum.
 
Last edited:
Physics news on Phys.org
  • #2
You were right in thinking that g stood for gravity, it simply is a matter of units. 9.8 represents the acceleration in m/s^2, whereas you're working with feet in this problem!
 
  • #3
Bah, so what would the correct # be?
 
  • #4
32 right?
 
  • #5
Right.
 
  • #6
Thank you very much. My test grades will finally get the justice they deserve.
 

1. How can precalculus be used to solve a football kicking problem?

Precalculus is used to analyze the variables involved in a football kicking problem, such as the distance to the goal, the angle of the kick, and the velocity of the ball. By using equations and trigonometric functions, precalculus can help determine the optimal trajectory for the kick.

2. What are the key components of a football kicking problem?

The key components of a football kicking problem include the distance to the goal, the angle of the kick, the velocity of the ball, and any external factors such as wind or obstacles. These variables can be represented by mathematical equations in precalculus.

3. How does precalculus help to find the optimal trajectory for a football kick?

Precalculus uses mathematical principles such as projectile motion and trigonometric functions to analyze the variables involved in a football kicking problem. By finding the optimal angle and velocity for the kick, precalculus can determine the trajectory that will result in the ball reaching the goal.

4. Can precalculus be used to solve different types of football kicking problems?

Yes, precalculus can be applied to various football kicking problems, such as field goals, punts, and kickoffs. The same principles and equations can be used, but the values for the variables may differ depending on the specific scenario.

5. What are some real-life applications of using precalculus to solve football kicking problems?

Precalculus can be used in real-life situations, such as in professional football, to help coaches and players make strategic decisions. It can also be used in training and practice to improve the accuracy and distance of kicks. Additionally, the principles of precalculus used in football kicking problems can be applied to other sports or activities involving projectile motion.

Similar threads

  • Introductory Physics Homework Help
2
Replies
38
Views
1K
  • Introductory Physics Homework Help
Replies
1
Views
2K
  • Introductory Physics Homework Help
Replies
5
Views
5K
  • Introductory Physics Homework Help
Replies
2
Views
799
  • Introductory Physics Homework Help
Replies
11
Views
1K
  • Introductory Physics Homework Help
Replies
25
Views
5K
  • Introductory Physics Homework Help
Replies
2
Views
1K
  • Introductory Physics Homework Help
Replies
3
Views
1K
  • Precalculus Mathematics Homework Help
Replies
2
Views
3K
  • Introductory Physics Homework Help
Replies
7
Views
2K
Back
Top