Do you feel more impact force when falling straight down or tipping over?

Question

Suppose you fall from the top of a ladder straight down. You will hit the ground with an amount of force. Now suppose that you fall over while holding onto the ladder, tipping over in an arc instead of falling straight down. You will hit the ground with another amount of force. Neglecting the mass of the ladder and air resistance, which impact will have the most force? Falling or tipping? This has been a bit of a debate between myself, my father, and my grandfather. I believe that they would fall with the same force because, relative to the ground, you start with the same amount of potential energy in both situations. My grandfather and father, however, guess that it would fall with around half the force because the force is dissipated somewhat by the forward motion and the support of the ladder. We would appreciate an answer from a third party to help us find the solution.

Answer 1

Great question. First, we must break the two scenarios down and find the force of impact for both.

For this, let's say

Your weight is 100lbs

The height of the drop 10ft

g = 9.8m/2

10 ft = 3.048 m

100lbs = 45.36kg

For Seaniro 1: Straight Down

v = √(2gh)

v = √(2 * 9.8 * 3.048)

v = 7.71 m/s

F = mv/t

F = (45.36 * 7.71) / 0.05

F = 6,996N

Scenario 2: Tipping over

w = √(3g)/L

w = √(3 * 9.8) / 1.8

w = 4.04 rad/s

v = w * L

v = 4.04 * 1.8

v = 7.27 m/s

F = mv/t

F = (45.36 * 7.27) / 0.02

F = 16,490N

Now, the actual force of impact from tipping over is greater than that of falling straight down. Since, assumingly if you hold on to the ladder while it tips, you will land on your side. So the force of impact will be felt over a larger surface area of your body. Whereas, falling straight down, you will land on your feet, thus, more force is felt in a smaller area.

While both are survivable, both are very dangerous. The risk of injury of fractures, internal organ damage, and broken bones is high with both. Please note that in the tipping-over scenario, this is slightly more dangerous as the risk of hitting your head is greater.