Final answer:
Using the projectile motion equation, the football kicked at an angle of 30° with a speed of 20 m/s will stay in the air for approximately 2.04 seconds, which rounds to 2 seconds.
Step-by-step explanation:
To determine the time a football stays in the air after being kicked, we need to analyze the vertical component of its motion. We can use the equation for the time of flight for a projectile launched at an angle which is derived from the kinematic equations. The relevant equation is:
t = (2 * v * sin(θ)) / g,
where t is the time of flight, v is the initial speed, θ is the launch angle, and g is the acceleration due to gravity (approximately 9.81 m/s2). Plugging the given values into the equation, we get:
t = (2 * 20 m/s * sin(30°)) / 9.81 m/s2,
Since sin(30°) is 0.5, the equation simplifies to:
t = (2 * 20 m/s * 0.5) / 9.81 m/s2,
t = 20 m/s / 9.81 m/s2,
t ≈ 2.04 seconds.
To the nearest second, the football will stay in the air for 2 seconds.