Final answer:
To calculate the force on a person at an acceleration of 30 g's, multiply their mass by the acceleration due to gravity. To calculate the distance traveled when brought to rest at this acceleration, use the equation for average acceleration.
Step-by-step explanation:
To calculate the force on a person accelerating at a rate of 30 g's, we can use Newton's second law of motion, which states that force equals mass times acceleration (F = ma). Given that the person's mass is 61 kg and the acceleration is 30 g's (where 1 g = 9.8 m/s²), we can calculate the force as follows:
F = 61 kg × 30 × 9.8 m/s² = 17,988 N
To calculate the distance traveled when brought to rest at this rate, we can use the equation for average acceleration (a = (v² - u²) / (2s)), where v is the final velocity (0 m/s), u is the initial velocity (92 km/hr converted to m/s), and a is the acceleration (-30 g's converted to m/s²). Solving for s, the distance traveled, we get:
s = (v² - u²) / (2a) = (0 - (92 km/hr × (1000 m/3600 s))²) / (2 × -30 × 9.8 m/s²) = 180.21 m