2025 PHS P2 Q4

A scientist measures the height of a mini rocket at different times after it launches. The height, \(h\), above the ground is measured in metres and the time, \(t\), is measured in seconds. The mini rocket was launched 45 m above the ground. The rocket returned to the ground 9 seconds after it had been launched.

The model of the motion is given as \(h=-12t^2+103t+45\).

1. Explain why the model is suitable for the measurements found.[2]
2. Find the range of values of \(t\) for which the height of the rocket above the ground is greater than 136 m.[3]
3. Explain whether the rocket can reach 300 m above the ground.[2]