Football is kicked up into the air with a velocity of 20m/s.

a. Determine the time the football is in the air.
b. Determine the maximum height the football would reach.
c. As the ball is kicked it encounters a weird horizontal wind that gives it a velocity of 5m/s. Determine the range the football would have.
d. Solve for the Resultant velocity that the football would have.

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To solve these problems, we can use the kinematic equations of motion for projectile motion.

a. Determine the time the football is in the air:
The time the football is in the air can be found using the equation:
time = 2 * (vertical velocity) / (acceleration due to gravity)

Since the only force acting on the football in the vertical direction is gravity, the vertical velocity at the highest point of its trajectory would be 0 m/s. Thus, the equation becomes:
time = 2 * (vertical initial velocity) / (acceleration due to gravity)

Given that the vertical initial velocity is 20 m/s and the acceleration due to gravity is approximately 9.8 m/s^2, we can substitute these values into the equation to find the time:
time = 2 * 20 m/s / 9.8 m/s^2 = 4.08 seconds (rounded to two decimal places)

Therefore, it will take approximately 4.08 seconds for the football to be in the air.

b. Determine the maximum height the football would reach:
The maximum height reached by the football can be calculated using the equation:
maximum height = (vertical initial velocity)^2 / (2 * acceleration due to gravity)

Substituting the given values:
maximum height = (20 m/s)^2 / (2 * 9.8 m/s^2) = 20.41 meters (rounded to two decimal places)

Therefore, the football would reach a maximum height of approximately 20.41 meters.

c. Determine the range the football would have:
The range of the football can be calculated using the equation:
range = horizontal velocity * time

Given that the horizontal velocity of the football is 5 m/s and the time of flight is approximately 4.08 seconds, we can calculate the range:
range = 5 m/s * 4.08 s = 20.4 meters (rounded to one decimal place)

Therefore, the football would have a range of approximately 20.4 meters.

d. Solve for the resultant velocity that the football would have:
To solve for the resultant velocity, we can use the Pythagorean theorem:
resultant velocity = √(horizontal velocity^2 + vertical velocity^2)

Given that the horizontal velocity is 5 m/s and the vertical velocity is 20 m/s, we can substitute these values into the equation:
resultant velocity = √((5 m/s)^2 + (20 m/s)^2) = √(25 m^2/s^2 + 400 m^2/s^2) = √425 m^2/s^2 = 20.62 m/s (rounded to two decimal places)

Therefore, the resultant velocity that the football would have is approximately 20.62 m/s.