Final answer:
To find the flight time of the ball, we need to break down the initial velocity into its horizontal and vertical components. Using the equation for vertical motion, we can find the time it takes for the ball to reach its maximum height. Doubling this time gives us the total flight time of the ball.
Step-by-step explanation:
To find the flight time of the ball, we need to first break down the initial velocity into its horizontal and vertical components. Since the ball is kicked at a 60-degree angle, the vertical component is given by 20 m/s * sin(60) = 17.32 m/s. The horizontal component is given by 20 m/s * cos(60) = 10 m/s. Next, we can use the vertical component to calculate the time it takes for the ball to reach its maximum height. The equation for the vertical motion of the ball is h = v0y * t - 0.5 * g * t^2, where h is the maximum height, v0y is the vertical component of the initial velocity, t is the time, and g is the acceleration due to gravity (-9.8 m/s^2). Setting h to 0 (since the ball starts and ends at the same height), we can solve for t. 0 = v0y * t - 0.5 * g * t^2, t * (v0y - 0.5 * g * t) = 0, t = 0 or v0y - 0.5 * g * t = 0, v0y - 0.5 * g * t = 0, 17.32 - 0.5 * 9.8 * t = 0, t = 17.32 / (0.5 * 9.8) = 3.54 s. This is the time it takes for the ball to reach its maximum height. The total flight time can be found by doubling the time to reach the maximum height: 2 * 3.54 s = 7.08 s. Therefore, the flight time of the ball is approximately 7.08 seconds.