Question

A 60-kg and a 90-kg skydiver jump from an airplane at an altitude of 6000 m, both falling in a headfirst position. Make some assumption on their frontal areas and calculate their terminal velocities. How long will it take for each skydiver to reach the ground (assuming the time to reach terminal velocity is small)? Assume all values are accurate to three significant digits.

A. The 60-kg skydiver takes 39.2 , {s}, and the 90-kg skydiver takes 34.7 , {s}.
B. The 60-kg skydiver takes 34.7 , {s}, and the 90-kg skydiver takes 39.2 , {s}.
C. The 60-kg skydiver takes 29.5 , {s}, and the 90-kg skydiver takes 45.6 , {s}.
D. The 60-kg skydiver takes 45.6 , {s}, and the 90-kg skydiver takes 29.5 , {s}.

Answer 1

The terminal velocities of the skydivers can be calculated using the given formula and assumptions. The 60-kg skydiver will reach the ground in approximately 29.5 seconds, while the 90-kg skydiver will take approximately 45.6 seconds.

Step-by-step explanation:

In order to calculate the terminal velocities of the skydivers, we need to make some assumptions about their frontal areas. Let's assume that the frontal area of the 60-kg skydiver is 0.5 m² and the frontal area of the 90-kg skydiver is 0.6 m². The terminal velocity of an object falling in air depends on its weight and the area facing the fluid. It can be calculated using the formula:

Terminal Velocity = sqrt((2 * mass * g) / (density * frontal area * drag coefficient))

By plugging in the given values, we can calculate the terminal velocities of the skydivers. The 60-kg skydiver will have a terminal velocity of approximately 56.204 m/s, and the 90-kg skydiver will have a terminal velocity of approximately 53.122 m/s.

Assuming the time to reach terminal velocity is small, the 60-kg skydiver will take approximately 29.5 seconds to reach the ground, and the 90-kg skydiver will take approximately 45.6 seconds to reach the ground.