(b) a police helicopter takes off straight up from the ground. it quickly ascends to several hundred feet…

Explanation:

Step1: Analyze take - off phase

The helicopter takes off straight up from the ground. So, the height of the helicopter increases with time. This is represented by a rising line on the height - time graph.

Step2: Analyze constant height phase

Then it flies straight ahead at a constant height for a few minutes. During this time, the height of the helicopter does not change with time, so the graph is a horizontal line.

Step3: Analyze return phase

Without changing height, it turns and flies toward headquarters. Since it is still at a constant height during this motion, the graph remains horizontal until it lands (not shown in the description but not relevant for the given motion analysis).

The correct graph is the one where the height first increases (rising line), then remains constant (horizontal line).

Answer:

The fourth graph (where the height first increases and then is constant as a horizontal line)