Solving a PreCalc Football Problem

[mandomansion]

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.

 

[cristo]

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?]

Those equations look fine to me; what part did you mean to put in italics?

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.

I can't check your answer if you don't give any working! You will need to work through the algebra by hand, and not just quote what your calculator tells you.

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.

I'm afraid we don't do homework for students here at PF, but rather offer guidance once the student has made an attempt on his or her own.

 

[Architeuthis Dux]

Hello! I am happy to help you solve this PreCalc football problem. First, let's go over the formulas you have provided. The formula for x(t) is correct, but for y(t), the -0.5gt^2 term represents the acceleration due to gravity, and the 3 represents the initial height of the ball. So the correct formula for y(t) would be: y(t) = -4.9t^2 + (50 * sin 65)t + 3. Make sure to use -4.9 as the value for g since it is in feet per second squared.

To find the max height of the ball, we need to find the vertex of the parabola described by the y(t) formula. This can be done by using the formula t = -b/2a, where a = -4.9 and b = 50 * sin 65. Plugging in these values, we get t = -50sin 65 / 2(-4.9) = 5.07 seconds. To find the max height, we can plug this value into the y(t) formula: y(5.07) = -4.9(5.07)^2 + (50 * sin 65)(5.07) + 3 = 107.69 feet.

To find how far the ball landed from Scott, we need to find the x-coordinate at the time when the ball hits the ground. This can be done by setting y(t) = 0 and solving for t. We get t = 10.2 seconds. Then, we can plug this value into the x(t) formula to get the distance the ball traveled horizontally: x(10.2) = (50 * cos 65)(10.2) = 190.18 feet.

Finally, to find how long the ball was in the air, we just need to find the time it takes for the ball to reach the ground. This is the same as finding the x-intercept of the parabola described by the y(t) formula. Using the quadratic formula, we get t = 10.2 seconds.

As for the mode settings on your TI-83 calculator, make sure to set it to degrees since we are using the angle in degrees. Also, make sure to use the correct units for time (seconds) and acceleration due to gravity (feet per second