Step 1: Understanding the Question:
The problem asks for the vertical displacement of an object moving under gravity until its velocity drops to zero at the peak.
Step 2: Key Formula or Approach:
We use the third equation of motion for constant acceleration:
\[ v^2 = u^2 - 2gh \]
Where \(u\) is initial velocity, \(v\) is final velocity, and \(h\) is height.
Step 3: Detailed Explanation:
Given: Initial velocity \(u = 20\ \text{m/s}\) and \(g = 10\ \text{m/s}^2\).
At the maximum height, the final velocity \(v = 0\).
Substituting the values:
\[ 0^2 = (20)^2 - 2(10)h \]
\[ 0 = 400 - 20h \]
\[ 20h = 400 \]
\[ h = \frac{400}{20} = 20\ \text{m} \]
Step 4: Final Answer:
The maximum height reached by the ball is 20 metres.