4400 Higher June 2006 Paper 4 Q15
15 A ball is dropped from a tower.
After \(t\) seconds, the ball has fallen a distance \(x\) metres.
\(x\) is directly proportional to \(t^2\).
When \(t = 2\), \(x = 19.6\)
(a) Find an equation connecting \(x\) and \(t\). (3)
(b) Find the value of \(x\) when \(t = 3\) (2)
(c) Find how long the ball takes to fall 10 m. (3)
| Scheme | Marks |
|---|---|
| \(x = kt^2\) or \(19.6 = k \times 2^2\) | M1 |
| \(k = 4.9\) | A1 |
| \(x = 4.9t^2\) oe | A1 |
| (3) |
Notes
M1: oe
A1: Allow \(x \propto 4.9t^2\) for A1
| Scheme | Marks |
|---|---|
| \(3^2 \times 4.9\) | M1 |
| \(x = 44.1\) | A1f |
| (2) |
Notes
A1f: Follow her (a) if of form \(kt^2\)
| Scheme | Marks |
|---|---|
| \(10 = 4.9t^2\) | M1 |
| \(t^2 = 10 / 4.9\) or 2.04… | M1 |
| 1.43 or 1.4 with wking | A1 |
| (3) | |
| (8 marks) |
Notes
M1: Follow her (a) if of form \(kt^2\)
A1: cao