Q: suppose the kick in example 3-5 is attempted 36m from thegoal post, whose crossbar is 3.00m above the ground. If thefootball is directed correctly

We are given:
- The distance from the kick to the goal post is $d=36\text{m}$.
- The height of the goal post's crossbar is $h=3.00\text{m}$.
To determine if the football will pass over the bar and be a field goal, we need to analyze the projectile motion of the football.
Let's consider the horizontal and vertical components of the motion separately.
1. Horizontal Component:
The horizontal motion of the football is not affected by gravity. Therefore, we can use the following equation to calculate the time of flight:
$\text{time}=\frac{d}{\text{horizontal velocity}}$
2. Vertical Component:
The vertical motion of the football is affected by gravity. We can use the following equation to calculate the maximum height reached by the football:
$\text{maximum height}=\frac{{\text{initial vertical velocity}}^2}{2g}$
where $g$ is the acceleration due to gravity.
To determine if the football will pass over the bar, we need to check if the maximum height reached by the football is greater than the height of the crossbar.
Now let's calculate the solution using LaTeX markup:
1. Horizontal Component:
The horizontal velocity of the football remains constant throughout its motion. We assume there is no air resistance, so the horizontal velocity is given by:
$\text{horizontal velocity}=\frac{d}{\text{time}}$
2. Vertical Component:
We need to calculate the initial vertical velocity to determine the maximum height reached by the football. The initial vertical velocity can be found using the equation of motion:
$\text{initial vertical velocity}=\sqrt{2gh}$
where $g=9.8{\text{m/s}}^2$ is the acceleration due to gravity.
Next, we can calculate the time of flight:
$\text{time}=\frac{d}{\text{horizontal velocity}}$
Finally, we can calculate the maximum height reached by the football:
$\text{maximum height}=\frac{{(\text{initial vertical velocity})}^2}{2g}$
If the maximum height is greater than the height of the crossbar ($h$), then the football will pass over the bar and be a field goal.

To determine whether the football will pass over the bar and be a field goal, we need to consider the height and trajectory of the kick.
Let's assume the football is kicked with an initial velocity $v$ and an angle $\theta$ above the horizontal. We can use the equations of projectile motion to analyze the motion of the football.
The horizontal and vertical components of the initial velocity can be calculated as:
$v_x=v·\cos (\theta )\text{and}{v}_y=v·\sin (\theta )$
where $v_x$ is the horizontal component and $v_y$ is the vertical component.
The time $t$ it takes for the football to reach the goalpost can be found using the vertical component:
$t=\frac{v_y}{g}$
where $g$ is the acceleration due to gravity (approximately $9.8{\text{m/s}}^2$).
Next, we can find the horizontal distance $d$ covered by the football during this time:
$d=v_x·t$
If the calculated horizontal distance $d$ is greater than or equal to the given distance of 36 m, the football will pass over the bar and be a field goal.
To find the values of $v$ and $\theta$, we need more information or additional equations from 'example 3-5.'

To solve this, we can use the concept of projectile motion. The football can be treated as a projectile that follows a parabolic trajectory.
Step 1: Calculate the initial vertical velocity ($v_{\text{y}}$) of the football.
Since the football is directed correctly between the goalposts, we can assume it will travel in a straight line horizontally without any acceleration. Therefore, the time taken to reach the goal post is the same as the time taken to reach the crossbar.
The vertical displacement of the football is the difference between the height of the crossbar and the initial height of the football. The initial height is 0 since the football is on the ground.
Using the equation:
$\Delta y=v_{\text{y}}t+\frac{1}{2}g{t}^2$
where $\Delta y$ is the vertical displacement, $t$ is the time of flight, and $g$ is the acceleration due to gravity (approximately $9.8{\text{m/s}}^2$), we can rewrite the equation as:
$h=v_{\text{y}}t+\frac{1}{2}g{t}^2\text{(equation 1)}$
Since the football is kicked horizontally, the initial vertical velocity is 0. Hence, the equation 1 becomes:
$h=\frac{1}{2}g{t}^2\text{(equation 2)}$
Solving equation 2 for $t$:
$t=\sqrt{\frac{2h}{g}}$
Plugging in the values, $h=3.00\text{m}$ and $g=9.8{\text{m/s}}^2$, we get:
$t=\sqrt{\frac{2\times 3.00}{9.8}}$
Step 2: Calculate the horizontal distance traveled by the football ($x$).
The horizontal distance traveled by the football can be calculated using the equation:
$x=vt$
where $v$ is the horizontal velocity of the football. Since there is no horizontal acceleration, the horizontal velocity remains constant throughout the motion.
To find $v$, we can use the equation:
$v=\frac{d}{t}$
where $d$ is the distance from the kick to the goal post. Plugging in the values, $d=36\text{m}$ and $t$ from step 1, we can calculate $v$.
Step 3: Determine if the football will pass over the bar.
To determine if the football will pass over the bar, we need to compare the maximum height reached by the football with the height of the crossbar.
The maximum height reached by the football can be calculated using the equation:
$H=\frac{v_{\text{y}}^2}{2g}$
where $H$ is the maximum height.
If $H>h$, then the football will pass over the bar and be a field goal. Otherwise, it will not.
Let's now calculate the values:
Step 1: Calculate $t$.
$t=\sqrt{\frac{2h}{g}}=\sqrt{\frac{2\times 3.00}{9.8}}\approx 0.782\text{s}$
Step 2: Calculate $v$.
$v=\frac{d}{t}=\frac{36}{0.782}\approx 46.07\text{m/s}$
Step 3: Calculate $H$.
$H=\frac{v_{\text{y}}^2}{2g}=\frac{0^2}{2\times 9.8}=0\text{m}$
Since $H=0\text{m}$, the maximum height reached by the football is 0, which is less than the height of the crossbar ($h=3.00\text{m}$). Therefore, the football will not pass over the bar and it will not be a field goal.
Therefore, the football will not be a field goal.