Reflection on Free Fall in Outer Space

How long would it take a rock falling from rest to reach a velocity of 19.1 m/s on each celestial body?

It would take __ sec on Celestial Body A and __ sec on Celestial Body B.

Answer:

It would take 4.95 seconds on Celestial Body A and 0.90 seconds on Celestial Body B for a rock falling from rest to reach a velocity of 19.1 m/s.

Reflecting on the equations for free fall near the surfaces of two celestial bodies in outer space, we see that the time it takes for a rock falling from rest to reach a velocity of 19.1 m/s differs between Celestial Body A and Celestial Body B.

For Celestial Body A, the time taken is 4.95 seconds, while for Celestial Body B, it only takes 0.90 seconds. This discrepancy is due to the respective equations that govern the free fall on each celestial body.

To find these times, we first need to calculate the time it takes for the rock to reach a velocity of 19.1 m/s on each celestial body. This involves differentiating the given equations with respect to time and solving for the time required to reach the desired velocity.

For Celestial Body A, the derivative of the equation with respect to time gives us the velocity as 3.86t. By setting this velocity equal to 19.1 m/s and solving for time, we find that it takes 4.95 seconds for the rock to reach the specified velocity.

On the other hand, for Celestial Body B, the velocity equation is 21.26t. Solving for time when the velocity is 19.1 m/s results in a time of 0.90 seconds for the rock to achieve the desired speed.

In conclusion, the different equations governing free fall near the surfaces of Celestial Body A and Celestial Body B lead to varying times for a rock falling from rest to reach a velocity of 19.1 m/s. This reflection highlights the importance of understanding the specific conditions of each celestial body when calculating such timeframes in outer space.