Question

There are many well-documented cases of people surviving falls from heights greater than 20.0 m. In one such case, a 55.0 kg woman survived a fall from a 10th floor balcony, 29.0 m above the ground, onto the garden below, where the soil had been turned in preparation for planting. Because of the "give" in the soil, which the woman compressed a distance of 15.0 cm upon impact, she survived the fall and was only briefly hospitalized.
a. Ignoring air resistance, what was her impact speed with the ground (in m/s)?
b. What was the magnitude of her deceleration during the impact in terms of g?
c. Assuming a constant acceleration, what was the time interval (in s) during which the soil brought her to a stop?
d. What was the magnitude of the impulse (in N · s) felt by the woman during impact?
e. What was the magnitude of the average force (in N) felt by the woman during impact?

Answer 1

a. Her impact speed was

$$v=\sqrt{2gh}=23.8\text{ m/s}.$$

b. The magnitude of her deceleration was

$$a=\frac{v^2}{2d}=\frac{gh}{d}=\frac{9.8\cdot29}{0.15}=\\ \space\\ =1895\text { m/s}^2,$$

or

$$a_g=(a/g)\cdot g=193g.$$

c. That time interval was

$$t=v/a=d\sqrt{\frac{2}{gh}}=0.0126\text{ s}.$$

d. The magnitude of the impulse

$$p=Ft=mat=m\sqrt{2gh}=1311\text{ N-s}.$$

e. The average force of impact:

$$F=ma=\frac{mgh}{d}=104207\text{ N}.$$