Final answer:
The ball takes approximately 4.08 seconds to travel from the release location to its highest point, and the total time the ball is in the air before it returns to the original height is approximately 8.16 seconds.
Step-by-step explanation:
When the ball is thrown upward with a speed of 40 m/s, we can calculate the time it takes to reach its highest point where the velocity becomes zero due to gravity. The acceleration due to gravity is approximately -9.81 m/s². Using the formula v = u + at (where v is the final velocity, u is the initial velocity, and a is the acceleration), we can set v = 0, u = 40 m/s, and a = -9.81 m/s² to solve for time (t).
The equation then becomes 0 = 40 + (-9.81)t, which simplifies to 0 = 40 - 9.81t. Solving for t gives us t = 40 / 9.81, which is approximately 4.08 seconds to reach the highest height (B). This is the time for the ball to go from the release location (A) to the highest point (B).
To find the total time the ball is in the air before it returns back to the original height (C), we consider that the upward journey and downward journey time are the same. Therefore, the total time in the air is twice the time taken to reach the highest point, which is 4.08 seconds multiplied by 2, giving us approximately 8.16 seconds.
Therefore, the correct answer is b) 4.08s, 8.16s.