A woman is reported to have fallen 161 ft from a building, landing on a metal ventilator box, which she crushed to a depth of 29 in. She suffered only minor injuries. Ignoring air resistance, calculate: (a) the speed of the woman just before she collided with the ventilator and (b) her average acceleration while in contact with the box. (c) Modeling her acceleration as constant, calculate the time interval it took to crush the box.

a) 31.02 m/s

b) - 653.24 m/s²

c) 50 ms

Explanation:

a) For a vertical movement, let's suppose that the woman fell by the rest, thus she's initial velocity v0 = 0 m/s. If she makes a distance (S) of 161 ft = 49.1 m, thus, her final velocity at the box, v is:

v² = v0² + 2aS

The acceleration is the gravity acceleration, 9.8 m/s².

v² = 2*9.8*49.1

v² = 962.36

v = √962.36

v = 31.02 m/s

b) She crushes the box until she stops, so her final velocity will be 0 m/s. The initial velocity is now 31.02 m/s, and S = 29 in = 0.7366 m

0 = 31.02² + 2a*0.7366

-1.4732a = 962.36

a = - 653.24 m/s² (the negative signal indicates that she's dessacelaranting)

c) The time can be calculate by:

v = v0 + at

0 = 31.02 - 653.24*t

653.24t = 31.02

t = 0.05 s = 50 ms