Final answer:
This response addresses a high school level physics question on projectile motion, detailing the steps to calculate the time it takes for a soccer ball to reach its peak, the maximum height achieved, the total time in flight, and the horizontal distance covered.
Step-by-step explanation:
The student is dealing with a projectile motion problem in Physics, where a soccer ball is kicked and its motion is analyzed in two dimensions: horizontal and vertical (x and y components).
Part A: Time to Reach the Top
To determine the time it takes for the ball to reach the top, we only consider the vertical component. Since the acceleration due to gravity (g) is -9.8 m/s2 (negative because it opposes the upward motion), we can use the equation v = u + at, where v is the final velocity (0 m/s at the top), u is the initial velocity (6.4 m/s), a is the acceleration (due to gravity, -9.8 m/s2), and t is the time. Rearranging for t, we find t = (0 m/s - 6.4 m/s) / -9.8 m/s2.
Part B: Maximum Height
The maximum height can be determined using the equation s = ut + 0.5at2, where s is the displacement (maximum height), using the time calculated in Part A for t.
Part C: Time to Fall to the Ground
The total time in the air is twice the time it takes to reach the top because of the symmetry of projectile motion in a vacuum (no air resistance).
Part D: Horizontal Distance Traveled
To find the horizontal distance (d), we use the horizontal velocity (10.4 m/s) and the total time the ball is in the air.