FOOTBALL. During a field goal attempt, the function h(d)= -0.02d+ 0.9d models the height, h(d) meters, of a football in terms of the horizontal distance, d meters, from where the ball was kicked. Find the horizontal distance the ball travels until it first hits the ground.
please,please I need your help.
much appreciated in advance.
Your fomula can be rewritten h = 0.88d and is obviously wrong. The football does not keep rising in a straight line.
A correct formula would have the form:
h = - g (d/Vxo)^2 + Vyo*(d/Vxo).
where Vxo is the horizontal velocity component (which remains constant) and Vyo is the initial vertical velocity component
I believe you should have written
h(d)= -0.02d^2+ 0.9d
This would correspond to a football kicked with a horizontal velocity component of 22.1 m/s and an initial vertical component of 19.9 m/s.
Anyway, to do the proplem, set
h(d)= -0.02d^2+ 0.9d = 0 and solve for d, and take the answer that is not zero. You will get 45 meters, which is about 50 yards. that is typical for a field goal.
THANK YOU!!
one mini problem: i haven't learned this yet.
and i don't own a graphing calculator..
i haven't learned "h = - g (d/Vxo)^2 + Vyo*(d/Vxo). " this yet. woops.
You don't need a graphing calculator to solve -0.02d^2+ 0.9d = 0
Divide both sides by d and use algebra
0.02 d = 0.9
one more step and you have d.
oh.alright. i think i get it!! thanks
Never mind worrying about the formula h = - g (d/Vxo)^2 + Vyo*(d/Vxo).
I was just trying to derive the correct formula using physics, since the formula you provided was wrong.
one more question. -0.02d^2+ 0.9d = 0
where does the "-" in -0.02^2+0.9=0 go?
The minus sign goes where it is. You dropped the d^2 and the d in your version. You can't do that.
Add 0.02d^2 to both sides and you get
0.9 d = 0.02d^2
You seem to be unfamiliar with the basic rules and notations of algebra, and I recommend some tutoring if that is the case.
I'd be happy to help with your question! To find the horizontal distance the ball travels until it first hits the ground, we need to determine when the height of the ball, h(d), equals zero.
The given function h(d) = -0.02d + 0.9d represents the height of the ball at a given horizontal distance, d.
To find when the ball hits the ground, we set h(d) equal to zero and solve for d:
0 = -0.02d + 0.9d
Combining the like terms:
0 = 0.88d
Since 0 multiplied by any number is always 0, we can conclude that d can be any value. In other words, the ball hits the ground at any horizontal distance from where it was kicked.
Therefore, the ball will travel indefinitely until it hits the ground.