Question

this question is based on circular motion in a vertical plane:
The maximum value of acceleration that the human body can safely tolerate for short time intervals is nine times that due to gravity. Calculate the maximum speed with which a pilot could safely pull out of a circular dive of radius 4.00m . the answer: 88.5m/s

Please help me find a solution to this problem. Thank you so very much for your time and effort:)

Answer 1

this question is based on circular motion in a vertical plane: The maximum value of acceleration that the human body can safely tolerate for short time intervals is nine times that due to gravity. Calculate the maximum speed with which a pilot could safely pull out of a circular dive of radius 4.00m. the answer: 88.5m/s

The force of inertia is act on a pilot when he moves on a circle. Its direction is opposite to the radius. So, when the pilot will be in the lowest point of trajectory, he will have the maximum weight, which equal to:

$$P = F _ {i} + F _ {g} = M \frac {v ^ {2}}{R} + M g$$

From the task, $P$ should be equal to $9Mg$ to find the maximum speed.

$$9 M g = M \frac {v ^ {2}}{R} + M g$$ $$9 g = \frac {v ^ {2}}{R} + g \rightarrow v = \sqrt {8 g R}$$ $$v = \sqrt {8 * 9 . 8 m / s ^ {2} * 4 m} = 1 7. 7 1 m / s$$

Answer: $v = 17.71 \, \text{m/s}$

Answer in the task is wrong