Question

Two sky divers jump from different planes at the same time.

Skydiver A jumps from a plane at 11,000 feet above the ground and descends at a rate of 15 feet per second, x.
Skydiver B jumps from a plane and after 60 seconds is 10,100 feet above the ground.
After 3 minutes, Skydiver B is 8,300 feet above the ground.
Which of the statements below is false about the skydivers?

a. Skydiver B descends at a rate of 12 feet per second" is false.
b. Skydiver A reaches the ground before Skydiver B.
c. Skydiver B descends at a faster rate than Skydiver A.
d. The height difference between Skydiver A and Skydiver B remains constant throughout the descent.

Answer 1

The false statement about the skydivers is that Skydiver A reaches the ground before Skydiver B. In fact, both skydivers descend at the same rate of 15 feet per second, indicating that they will reach the ground at the same time if they started at the same altitude.

Step-by-step explanation:

Firstly, let's determine the rate of descent for Skydiver B. The descent in 60 seconds is 11,000 feet - 10,100 feet = 900 feet. Therefore, the rate of descent for Skydiver B in the first 60 seconds is 900 feet ÷ 60 seconds = 15 feet per second. Now, let's calculate the rate of descent from 60 seconds to 180 seconds (3 minutes). The additional descent is 10,100 feet - 8,300 feet = 1,800 feet over a period of 120 seconds. So the rate during this period is 1,800 feet ÷ 120 seconds = 15 feet per second. Hence, we discover that Skydiver B descends at a rate of 15 feet per second, not 12 feet per second as proposed by statement a.

Going further, if Skydiver A descends at a constant rate of 15 feet per second, it will take her 11,000 feet ÷ 15 feet/second = 733.33 seconds to reach the ground. Skydiver A and Skydiver B are descending at the same rate which means they will reach the ground at the same time if they started from the same altitude. However, since Skydiver B was at a lower altitude after 60 seconds, it can be inferred that he started at a lower altitude than Skydiver A, hence statement b is false.

Meanwhile, statement c is incorrect because both skydivers are descending at the same rate. Lastly, statement d infers that the height difference remains constant, but this cannot be true since both are descending at the same rate but started from different altitudes. The height difference would decrease over time until both reach the ground.