Final answer:
It would take approximately 63.87 seconds for the freely falling body to strike the ground from a height of 20 kilometers.
Step-by-step explanation:
To find the time it takes for a freely falling body to strike the ground when dropped from a height of 20 kilometers, we can use the equations of motion. The key equation for this situation is:
Vf = Vi + gt
Where Vf is the final velocity (which will be 0 m/s when the body hits the ground), Vi is the initial velocity, g is the acceleration due to gravity (which is approximately 9.8 m/s²), and t is the time taken.
Since the body is dropped (meaning its initial velocity is 0 m/s), the equation simplifies to:
0 = 0 + 9.8t
Solving for t, we get:
t = √(2h/g)
Substituting the given values of h = 20 kilometers and g = 9.8 m/s², we can calculate:
t = √(2 * 20,000 / 9.8) = √(40,000 / 9.8) = √4081.63 ~ 63.87 seconds
Therefore, it would take approximately 63.87 seconds for the freely falling body to strike the ground.