Higher June 2017 Paper 2 Q22
22 A ball, dropped vertically, falls \(d\) metres in \(t\) seconds.
- \(d\) is directly proportional to the square of \(t\).
- The ball drops 45 metres in the first 3 seconds.
How far does the ball drop in the next 7 seconds? [4 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 | ||
| \(d = kt^2\) or \(45 = k \times 3^2\) or \(45 \div 9\) | M1 | oe equation |
| \(d = 5t^2\) or \((k =)\ 5\) | M1dep | oe equation 245 implies M2 |
| their \(5 \times 10^2\) or 500 | M1dep | oe M3 \(\left(\dfrac{10}{3}\right)^2 \times 45\) oe |
| 455 | A1 | |
| Alternative method 2 | ||
| \(kd = t^2\) or \(k \times 45 = 3^2\) or \(9 \div 45\) | M1 | oe equation |
| \(0.2d = t^2\) or \((k =)\ 0.2\) | M1dep | oe equation 245 implies M2 |
| \(10^2 \div\) their 0.2 or 500 | M1dep | oe M3 \(45 \div \left(\dfrac{3}{10}\right)^2\) oe |
| 455 | A1 | |
Additional guidance
| \(d \propto t^2\) with no further valid working | Zero |
| \(d = kt\) or \(d = kt^3\) or \(d = \dfrac{k}{t^2}\) etc not recovered | Zero |
| 45 : 9 with no further valid working | Zero |
| \(d = 5t^2\) or \((k =)\ 5\) scores M2 even if not subsequently used | M2 |
| \(d = kt^2\) or \(45 = k \times 3^2\) or \(45 \div 9\) scores M1 even if not subsequently used | M1 |
| \(0.2d = t^2\) or \((k =)\ 0.2\) scores M2 even if not subsequently used | M2 |
| \(kd = t^2\) or \(k \times 45 = 3^2\) or \(9 \div 45\) scores M1 even if not subsequently used | M1 |
| Allow use of other letters |