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A football is kicked at an angle of 30° with a speed of 20 m/s. To the nearest second, how long will the ball stay in the air? A. 1s B. 2 s C. 3 s D. 4 s

User Robgraves
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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.

User Schrieveslaach
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