Question

23. The human body can survive an acceleration trauma accident (sudden stops), if the

magnitude of the acceleration is less than 250

2
. If you are in an automobile accident
with an initial speed of 105 km/h and you are stopped by an airbag that inflates from the
dashboard, over what distance must the airbag stop for you to survive the crash?

Answer 1

To survive the crash in an automobile accident with an initial speed of 105 km/h, the airbag must stop you over a distance of approximately 1.46 meters.

Step-by-step explanation:

In order to survive a sudden stop in a car accident, the magnitude of the acceleration must be less than 250g. To calculate the distance over which the airbag must stop you, we need to convert the initial speed into m/s and use the formula:

distance = (initial speed)^2 / (2 * acceleration)

First, let's convert the initial speed of 105 km/h into m/s. 1 km/h is equal to 0.2778 m/s, so 105 km/h is equal to 29.17 m/s.

Using the formula, we can calculate the distance:

distance = (29.17 m/s)^2 / (2 * 250g)

Since the acceleration due to gravity is approximately 9.8 m/s^2, we can convert 250g into m/s^2 by multiplying it by 9.8 to get:

distance = (29.17 m/s)^2 / (2 * 250 * 9.8 m/s^2)

Simplifying the equation gives:

distance = 29.17^2 / (2 * 250 * 9.8) meters

Calculating this expression gives a distance of approximately 1.46 meters.