Question

a helicopter comes down for landing and descends at a constant rate. while it is on the ground, it picks up two passengers. then, the helicopter takes off and ascends at a constant rate. the helicopter’s elevation increases at a rate of 600 feet per minute. the helicopter is at an elevation of 600 feet. it took the helicopter 600 minutes to take off.

Explanation:

To determine the correct statements, we analyze the graph:

Analyzing the first statement:

The ascending part of the graph (after \( x = 16 \)) goes from elevation \( 800 \) feet to \( 3200 \) feet. The time taken for this ascent is \( 20 - 16 = 4 \) minutes. The change in elevation is \( 3200 - 800 = 2400 \) feet. The rate of ascent is \( \frac{2400}{4} = 600 \) feet per minute. So, the first statement is correct.

Analyzing the second statement:

When the helicopter is on the ground (horizontal line), its elevation is \( 800 \) feet, not \( 600 \) feet. So, the second statement is incorrect.

Analyzing the third statement:

The helicopter takes off at \( x = 16 \) minutes (end of the horizontal segment). The time to take off is not \( 600 \) minutes (the graph's x - axis is in minutes, and the take - off happens within a few minutes, not 600). So, the third statement is incorrect.

• For the first statement, calculate the rate of ascent using the change in elevation and time for the ascending segment. The change in elevation is \( 3200 - 800 = 2400 \) feet and time is \( 20 - 16 = 4 \) minutes. The rate \( \frac{2400}{4}=600 \) feet per minute, so it is correct.
• For the second statement, the horizontal segment (helicopter on the ground) has an elevation of 800 feet, not 600, so it is incorrect.
• For the third statement, the take - off starts at \( x = 16 \) minutes, and the time to take off is not 600 minutes (the x - axis scale is in minutes and the take - off occurs in a short time), so it is incorrect.

Answer:

The helicopter’s elevation increases at a rate of 600 feet per minute.