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A woman fell 144 ft from the top of a building, landing on the top of a metal ventilator box, which she crushed to a depth of 18 in. She survived without serious injury. What acceleration (assumed uniform) did she experience during the collision? Express your answer in terms of g.

A woman  fell  144 ft from  the top of a building,  landing  on the top of a metal  ventilator  box,  which  she crushed  to a depth  of 18 in.  She  survived  without  serious  injury. What  acceleration (assumed   uniform)   did  she  experience   during   the  collision? Express  your  answer  in terms  of g.

Grade:10

1 Answers

Jitender Pal
askIITians Faculty 365 Points
6 years ago
From the equation of kinematics, we have
235-721_100.PNG
Where vy represents the final speed of the woman, a is her acceleration, voy the initial speed and t the time taken by the woman to attain the final speed vy .
From the second equation, the time t is given as:
235-1847_111.PNG
Substitute the value in first equation235-2243_102.PNG
Since the woman accelerates under the action of gravity and we take the convention of downward motion to be positive, we can equate a = g in the equation above as:
235-518_103.PNG
If we assume that the distance travelled by the woman during collision is y’ , the speed of the woman just before the contact is v’0y , and the final speed after the collision is v’y , such that she experience an acceleration a , then equation (1) can be written as:
235-2208_104.PNG
Since the woman will come to rest after colliding, her final speed v’y is zero. Also the initial speed before collision is equal to vy calculated above.
Given that the woman crushes the ventilator to a depth of 18 in, the height y’ can be equated too as 18 in.
Substitute the appropriate values in the equation above,

235-227_105.PNG
To calculate the acceleration in terms of g , divide and multiply the acceleration by it to have,
235-2206_106.PNG
Round of to two significant figures,
a = - 96g
It is important to note that the negative sign in the expression above accounts for the fact that the woman decelerates and the acceleration vector is in the direction opposite to the direction of the initial velocity vector.
Therefore the acceleration experienced by the woman is 96g.

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