Final answer:
Using the principles of projectile motion, Sally's soccer ball is estimated to travel approximately 41 meters when kicked at a 20 m/s initial speed and a 45-degree angle. The closest answer from the options provided is B. 40 meters.
Step-by-step explanation:
To determine how far Sally's soccer ball goes when kicked at an angle of 45 degrees with an initial speed of 20 m/s, we can use the physics of projectile motion. In projectile motion, the horizontal and vertical components of the motion are independent. The initial velocity can be broken down into horizontal (Vx) and vertical (Vy) components using trigonometric functions. For an angle of 45 degrees, these components will be equal because sin(45 degrees) = cos(45 degrees) = 0.7071 approximately.
The horizontal velocity (Vx) is the initial velocity (V) times the cosine of the angle (cos(45 degrees)): Vx = 20 m/s * 0.7071 = 14.14 m/s. The vertical velocity (Vy) is the initial velocity (V) times the sine of the angle (sin(45 degrees)): Vy = 20 m/s * 0.7071 = 14.14 m/s.
The time (t) the ball is in the air is determined by the vertical motion. Using the equation Vy = gt, where g is the acceleration due to gravity (9.81 m/s^2), we can solve for t. However, since we are looking for the total time in air, we consider that the ball has to go up and then come down, so we double the time it takes to reach the maximum height. Therefore, t = 2Vy/g = 2 * 14.14 m/s / 9.81 m/s^2 ≈ 2.9 seconds.
Finally, the range of the projectile is the horizontal velocity (Vx) times the total time (t) in the air. Range = Vx * t = 14.14 m/s * 2.9 s ≈ 41 meters.
So the soccer ball travels approximately 41 meters, which means the correct answer is B. 40 meters, since we are selecting the closest option provided.