Higher November 2024 Paper 3 Q17
17 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. [4 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 | ||
| \(d \propto t^2\) or \(d = kt^2\) or \(20 = k \times 2^2\) or \(k = 20 \div 4\) | M1 | oe equation |
| \(d = 5t^2\) or \(k = 5\) | M1dep | oe equation |
| \((t =)\sqrt{300 \div \text{their } 5}\) or \((t =)\sqrt{60}\) | M1dep | oe eg \((t =)2\sqrt{15}\) dep on M2 |
| [7.7, 7.75] | A1 | |
| Alternative method 2 | ||
| \(d \propto t^2\) or \(kd = t^2\) or \(k \times 20 = 2^2\) or \(k = 4 \div 20\) | M1 | oe equation |
| \(0.2d = t^2\) or \(k = 0.2\) | M1dep | oe equation |
| \((t =)\sqrt{\text{their } 0.2 \times 300}\) or \((t =)\sqrt{60}\) | M1dep | oe eg \((t =)2\sqrt{15}\) dep on M2 |
| [7.7, 7.75] | A1 | |
Additional guidance
Allow consistent use of other letters
\(d \propto kt^2\) is M0 unless recovered