Answer:
the football will pass over the crossbar and be a field goal.
Step-by-step explanation:
To determine whether the football will pass over the crossbar and be a field goal, you can use the equations of projectile motion. The key parameters are the initial velocity, angle, distance to the goalposts, and the height of the crossbar.
The horizontal distance traveled by the football (range) can be calculated using the following formula:
Range (R) = (v^2 * sin(2θ)) / g
Where:
- v is the initial velocity (20.0 m/s).
- θ is the angle above the ground (37°), which should be converted to radians.
- g is the acceleration due to gravity (approximately 9.81 m/s²).
First, convert the angle to radians:
θ = 37° * (π/180) ≈ 0.645 radians
Now, plug in the values and calculate the range:
R = (20.0 m/s)^2 * sin(2 * 0.645) / 9.81 m/s²
R ≈ 68.6 meters
The goalposts are 32.0 meters away from the kicker. To be a successful field goal, the football must travel a horizontal distance of 32.0 meters and reach a height of at least 3.00 meters (the height of the crossbar). From the calculated range, the football clearly travels far enough horizontally, but you also need to find the maximum height it reaches to see if it clears the crossbar.
The formula for the maximum height (H) is:
H = (v^2 * (sin(θ))^2) / (2 * g)
Plug in the values:
H = (20.0 m/s)^2 * (sin(0.645))^2 / (2 * 9.81 m/s²)
H ≈ 7.75 meters
The football reaches a maximum height of approximately 7.75 meters, which is well above the 3.00-meter crossbar. Therefore, the football will pass over the crossbar and be a field goal.