Sure, I'd be happy to help explain this problem to you! Projectile motion is a type of motion where an object, in this case a football, is launched or thrown at an angle and travels through the air under the influence of gravity. This type of motion can be broken down into two components: horizontal and vertical motion.
In this scenario, the football is kicked at an angle of 50 degrees. This angle is measured from the horizontal ground. The initial speed, or velocity, of the ball can be calculated using the components of the initial velocity in the horizontal and vertical directions. The horizontal component of the initial velocity can be found by using the formula v₀x = v₀cosθ, where v₀ is the initial velocity and θ is the angle of launch. In this case, v₀x = v₀cos50 = 14.1 m/s.
The vertical component of the initial velocity can be found by using the formula v₀y = v₀sinθ, where v₀ is the initial velocity and θ is the angle of launch. In this case, v₀y = v₀sin50 = 11.4 m/s.
Now that we have the initial velocity components, we can use them to solve for the other parts of the problem. The time of flight, or how long the ball is in the air, can be found using the formula t = 2v₀y/g, where g is the acceleration due to gravity (9.8 m/s²). In this case, t = 2(11.4)/9.8 = 2.2 seconds.
To find the maximum height that the ball reaches, we can use the formula h = v₀y²/2g. This formula represents the vertical displacement of the ball at its highest point. In this case, h = (11.4)²/2(9.8) = 5.94 meters.
So, to recap, we were able to find the initial speed of the ball using the given angle of launch and distance traveled. We also found the time of flight and maximum height reached by using the initial velocity components and the acceleration due to gravity. I hope this explanation helps you understand and solve similar projectile motion problems in the future!