How to Calculate Average Acceleration in a Fall?

[Melchior25]

So here is the question I'm stuck on.

A woman is reported to have fallen 112 ft from a building, landing on a metal ventilator box, which she crushed to a depth of 24 in. She suffered only minor injuries.

Calculate the magnitude of her average acceleration while in contact with the box.

I know average accel. = (delta v) / (delta t)

I calculated the speed of the woman just before she collided with the box to be 84.664 ft/s.

Although I'm a bit lost on how to calculate the avg. acceleration because I'm not sure what equation I should use to calculate (t).

 

[Doc Al]

Try expressing delta t in terms of delta v and the distance.

(You can also take advantage of kinematic relationships that directly relate speed, distance, and acceleration.)

 

[Moetasim]

I would first start by identifying the known values in this situation. We know that the woman fell 112 ft and landed on a metal ventilator box, crushing it to a depth of 24 in. We also know that she suffered only minor injuries.

To calculate the average acceleration, we need to use the equation a = (vf - vi) / t, where vf is the final velocity, vi is the initial velocity, and t is the time.

We have already calculated the final velocity to be 84.664 ft/s, and we can assume that the initial velocity was 0 ft/s since the woman was falling. Therefore, our equation becomes a = (84.664 ft/s - 0 ft/s) / t.

To calculate t, we can use the equation s = ut + 1/2at^2, where s is the displacement (in this case, 112 ft), u is the initial velocity (0 ft/s), and a is the acceleration (which we are trying to find). Rearranging this equation, we get t = √(2s/a).

Plugging in our known values, we get t = √(2 * 112 ft / a).

Now, we can substitute this value of t into our original equation for average acceleration: a = (84.664 ft/s - 0 ft/s) / √(2 * 112 ft / a).

Simplifying, we get a = 84.664 ft/s / √(224 ft/a).

To find the magnitude of the average acceleration, we can take the absolute value of this equation, since acceleration is a vector quantity. Therefore, the magnitude of the average acceleration is |a| = 84.664 ft/s / √(224 ft/a).

Using a calculator, we can solve for a and find that the magnitude of the average acceleration is approximately 30.023 ft/s^2.

This means that the woman experienced an average acceleration of 30.023 ft/s^2 while in contact with the metal ventilator box. This value is relatively high, which could explain why she suffered minor injuries despite falling from a significant height.