A stone falls vertically from 300 metres above ground.

• The stone falls d metres in t seconds.
• d is directly proportional to the square of t.
• The stone falls 20 metres in the first 2 seconds.
  Work out the total time taken for the stone to reach the ground.

The problem involves direct proportion. Step 1: Set up the proportionality equation. "d is directly proportional to the square of t" means d ∝ t². We can write this as an equation with a constant of proportionality, k: d = kt² Step 2: Find the constant k. We are given that the stone falls 20 metres (d=20) in 2 seconds (t=2). We substitute these values into our equation to find k. 20 = k * (2)² 20 = k * 4 k = 20 / 4 = 5 Step 3: Write the specific formula. Now that we know k=5, our formula is: d = 5t² Step 4: Solve for the required time. We want to find the time it takes for the stone to reach the ground, which is a fall of 300 metres (d=300). We use our formula and solve for t: 300 = 5t² Divide both sides by 5: t² = 300 / 5 t² = 60 Take the square root of both sides: t = √60 ≈ 7.746 seconds. Rounding to a suitable degree of accuracy, for example, 3 significant figures, gives 7.75 seconds.