Your favorite team is attempting a field goal. The ball is kicked at an angle of 45 degrees with the field. The ball covers a horizontal distance of 85 inches before the kick is blocked. What is the minimum height the opposing team's player can be to block the kick?
In a 45-45-90 triangle, the height is the same as the width.
So, the opponent cannot be over 85 inches tall. No problem; that's 7'1". That's if he plans on blocking the kick with his head . . .
Of course, what it really means is that the opponent cannot reach any higher than 85". Someone in the 6' height range can usually reach up to about 96 inches high.
So, our player needs to be somewhat shorter: about 65" or so.
And, that's assuming he isn't going to try and jump up to block the kick.
To find the minimum height the opposing team's player can be to block the kick, we need to analyze the motion of the projectile.
When the ball is kicked, it follows a parabolic path known as projectile motion. In this case, the projectile motion can be broken down into horizontal and vertical components.
First, let's focus on the horizontal component. The ball covers a horizontal distance of 85 inches before being blocked. Since there is no horizontal acceleration acting on the ball, the horizontal component of the ball's velocity remains constant throughout its flight.
Now, let's consider the vertical component. The ball is kicked at an angle of 45 degrees with the field, meaning it has an initial velocity that is split equally between the vertical and horizontal directions. Since there is no horizontal acceleration, the vertical motion is affected by gravity.
To calculate the minimum height the opposing team's player can be, we need to determine the time it takes for the ball to cover the horizontal distance of 85 inches. We can use the horizontal component of velocity and the given distance to find the time:
Distance = Velocity * Time
85 inches = Velocity * Time
Next, we need to determine the time it takes for the ball to reach its highest point. At the highest point, the vertical component of velocity will be zero because the ball momentarily stops before descending due to gravity.
We can use the vertical component of velocity and the acceleration due to gravity to calculate the time it takes to reach the highest point:
Vertical Component of Velocity = Initial Velocity * sin(angle)
0 (at highest point) = Initial Velocity * sin(45 degrees) - (Acceleration due to Gravity * Time)
Now, we have two equations with two unknowns (Velocity and Time). We can solve these equations simultaneously to find the values.
Once we have the time it takes for the ball to reach the highest point, we can calculate the vertical distance traveled during this time:
Vertical Distance = (Vertical Component of Velocity * Time) - (0.5 * Acceleration due to Gravity * Time^2)
Finally, the minimum height the opposing team's player can be to block the kick is equal to the vertical distance traveled during this time.