A very silly person, intent on catching pigeons on the roof of an apartment building, trips and falls a distance of 43.0 m. She lands on a metal garbage can, crushing it to a depth of 0.457 m and walks away without having been seriously hurt. What acceleration did she experience during the collision?

Question

A very silly person, intent on catching pigeons on the roof of an apartment building, trips and falls a distance of 43.0 m. She lands on a metal garbage can, crushing it to a depth of 0.457 m and walks away without having been seriously hurt. What acceleration did she experience during the collision?

Answer 1

To find the acceleration during the collision, we need to use the following equation:

acceleration = (change in velocity) / (time)

Since we are given the distance fallen and the depth of the garbage can, we can calculate the change in velocity during the collision.

First, we need to find the initial velocity of the person just before the collision. We can assume the person starts from rest, so the initial velocity (u) is 0 m/s.

Next, we need to find the final velocity of the person just after the collision. We can use the equation for free fall to calculate the final velocity (v) when falling a distance (s):

v^2 = u^2 + 2as

where:
v = final velocity
u = initial velocity
a = acceleration due to gravity (approximately 9.8 m/s^2)
s = distance fallen

Plugging in the given values:

v^2 = 0^2 + 2 * 9.8 * 43.0

v^2 = 0 + 843.6

v^2 = 843.6

v ≈ 29.01 m/s

Now, let's find the change in velocity during the collision:

change in velocity = final velocity - initial velocity

change in velocity = 29.01 - 0

change in velocity = 29.01 m/s

Next, we need to find the time taken during the collision. We can use the following equation of motion:

s = ut + (1/2)a*t^2

where:
s = depth of the garbage can
u = initial velocity
t = time taken
a = acceleration

Plugging in the given values:

0.457 = 0 * t + (1/2) * acceleration * t^2

0.457 = (1/2) * acceleration * t^2

0.914 = acceleration * t^2

Now, since the person walks away without serious injury, we can assume that the collision time is very short, and we can neglect the effect of gravity during this time. Therefore, the acceleration experienced during the collision is equal to the acceleration due to the compression of the garbage can.

Plugging in the value of time (t ≈ 0), we get:

0.914 = acceleration * 0

Since any number multiplied by 0 is equal to 0, we can conclude that the acceleration experienced during the collision is 0 m/s^2.