Question

A woman is reported to have fallen 132 ft from a building, landing on a metal ventilator box, which she crushed to a depth of 29 in. She suffered only minor injuries. (a) Neglecting air resistance, calculate the speed of the woman just before she collided with the ventilator box. ft/s (b) Calculate her average acceleration while in contact with the box ft/s2 (c) [Not Graded] Calculate the time it took to crush the box.

Answer 1

a) Please note that by conservation of energy principle, the potential energy at height is converted to kinetic energy on fall.

So,
Potential energy = mgh = $9.8 \times 132 \times 0.305 m$ = 395 m J [ 1 ft =0.305 meter]
Kinetic Energy = $\frac{1}{2} mv^{2}$
Now equating both as per conservation of energy principle.
$\frac{1}{2} mv^{2} = 395m$
Solving, we get
v = $\sqrt{790} m/s$ = 28.11 m/s = 92.22 ft/s [ 1m/s = 3.281 ft/s]

b) Now,
initial velocity while she touches the box is 92.22ft/s, and she crushes to depth of 29 inches = 2.42 ft
Also,note that final velocity will be 0m/s as she will stop after penetrating to depth of 2.42 ft

By newton's law,
$v^{2}=u^2+2as$ where s is distance, a is average acceleration, u and v are initial and final velocities respectively.
$0 ft/s=(92.22 ft/s)^2+2a \times 2.42 ft$
Solving, we get
$a = -1757.13 ft/s^2$

c) Time it took o crush the box an be obtained by using newton's law of motion
v =u +at
$0 ft/s =92.22 ft/s+ ( -1757.13 ft/s^2) t$
$t=\frac{92.22 ft/s}{ ( -1757.13 ft/s^2)}$

t = 0.05 s