Upon impact, bicycle helmets compress, thus lowering the potentially dangerous acceleration experienced by the head. A new kind of helmet uses an airbag that deploys from a pouch worn around the rider's neck. In tests, a headform wearing the inflated airbag is dropped onto a rigid platform; the speed just before impact is 6.0 m/s. Upon impact, the bag compresses its full 12.0 cm thickness, slowing the headform to rest. What is the acceleration, in g's, experienced by the headform? (An acceleration greater than 60g is considered especially dangerous.)

This is approximately 16 g's.

Explanation:

For the person’s head to stop falling, the rigid platform must exert a force that is equal to the sum of weight and force that caused the velocity to decrease from 6 m/s to 0 m/s.

Weight = m * -9.8

Let’s use the following equation to determine the acceleration.

vf^2 = vi^2 + 2 * a * d

0 = 36 + 2 * a * 0.12

a = -36 ÷ 0.24 = -150 m/s^2

The acceleration is negative, because it caused the velocity to decrease.

Total acceleration = -159.8 m/s^2

To determine the number of g, divide this by -9.8.

N g’s = -159.8 ÷- 9.8

This is approximately 16 g's.

we have been given a quadratic function and we need to restrict the domain such that it becomes a one to one function.

we know that vertex of this quadratic function occurs at (5,2).

further, we know that range of this function is .

if we restrict the domain of this function to either or , it will become one to one function.

let us know find its inverse.

upon interchanging x and y, we get:

let us now solve this function for y.

hence, the inverse function would be if we restrict the domain of original function to and the inverse function would be if we restrict the domain to .