The initial velocity of the football can be calculated using the following formula:
v0 = v * cos(θ)
Where v is the initial velocity of the football and θ is the angle at which it is thrown. In this case, v represents the total velocity of the football, so the initial velocity would be v0 = v * cos(43).
The total time the football stays in the air can be calculated using the following formula:
t = (2 * v * sin(θ)) / g
Where t is the total time, v is the initial velocity, θ is the angle at which it is thrown, and g is the acceleration due to gravity (9.8 m/s2). In this case, the total time would be t = (2 * v * sin(43)) / 9.8.
The maximum height that the football will reach can be calculated using the following formula:
h = (v2 * sin2(θ)) / 2g
Where h is the maximum height, v is the initial velocity, θ is the angle at which it is thrown, and g is the acceleration due to gravity (9.8 m/s2). In this case, the maximum height would be h = (v2 * sin2(43)) / (2 * 9.8).
The horizontal distance the football will travel can be calculated using the following formula:
d = (v2 * sin(2θ)) / g
Where d is the horizontal distance, v is the initial velocity, θ is the angle at which it is thrown, and g is the acceleration due to gravity (9.8 m/s2). In this case, the horizontal distance would be d = (v2 * sin(86)) / 9.8.
Air resistance, also known as drag, can affect the motion of the football by slowing it down as it travels through the air. This means that the football will not reach the same maximum height or travel the same horizontal distance as it would in a vacuum. The amount of air resistance also depends on the shape and size of the football, as well as the density of the air and the speed at which it is traveling.