Question

Amber falls out of the 17th floor of a building. The window is 144 ft about a metal ventilator box. Upon impact, he crushes it to a depth of 40 in. What was his speed before impact? What was his average acceleration when colliding with the box? How long did the collision last? Did he live, blackout, or die? *Convert 144 ft to meters.

Answer 1

144 feet = 43.8912 metres
Final speed: 66mph (29m/s)
Time to fall: 3 seconds.

Average acceleration at instant of impact will be acceleration due to gravity, which is about 9.81ms^2.
There is not enough information to determine the deceleration during impact, nor the duration til he stopped, however assuming he didn't bounce, the collision lasted until he got up and walked away or was carried off, depending on whether he survived or not.

A woman has been known to survive a fall of 10160 metres (Vesna Vulovic), but this is not typical. A fall of ten metres can easily kill you.

Answer 2

What was his average acceleration when colliding with the box?

By the work-energy theorem, the change in kinetic energy is equal to the work done in deceleration, which is Fd, F being the force and d the distance over which the force is applied in the direction of the force.

Now, kinetic energy, KE is given by
\[ KE = \frac{1}{2} mv^2 \]
and after the work is done the kinetic energy is zero. Therefore the change in KE is the negative of the KE just as she impacts. Therefore
\[ Fd = (ma)d = \frac{1}{2} mv^2 \implies a = \frac{1}{2} \frac{v^2}{d} \]
You know d and you know v. Use this to calculate a.