Step 1: Understanding the Question:
We are asked to find the time taken for a ball to fall back to its starting point (downward journey), given the time it took for its upward journey.
Step 2: Key Formula or Approach:
The key principle here is the symmetry of motion under constant gravitational acceleration, assuming air resistance is negligible. For an object thrown vertically upwards from a certain point, the time it takes to reach its maximum height (time of ascent) is equal to the time it takes to fall from that maximum height back to the original starting point (time of descent).
Time of Ascent = Time of Descent
Step 3: Detailed Explanation:
The problem states that the time for the upward journey (time of ascent) is 10 seconds.
Given: \( t_{upward} = 10 \, \text{s} \).
Based on the principle of symmetry of motion:
\( t_{downward} = t_{upward} \)
Therefore, \( t_{downward} = 10 \, \text{s} \).
The initial velocity of 5 m/s is extra information. Note that this information is inconsistent with the time of flight (using \(g \approx 10 \, \text{m/s}^2\), time to peak height would be \(t = v/g = 5/10 = 0.5\) s), but we must follow the primary information given, which is the 10 s journey time.
Step 4: Final Answer:
The downward journey will take the same amount of time as the upward journey, which is 10 seconds. Therefore, option (B) is correct.