To calculate the impact velocity of the ball bearing when it touches the ground after being dropped from a height of 500 feet (approximately 152.4 meters), we can use the principles of physics.
First, we need to calculate the velocity of the ball bearing just before it hits the ground using the equations of motion. We'll assume that air resistance is negligible since the ball bearing is small and dense.
The initial velocity (u) of the ball bearing is 0 m/s (since it's dropped).
The acceleration due to gravity (g) is approximately 9.81 m/s^2.
The distance fallen (s) is 152.4 meters.
We can use the equation of motion:
\[ v^2 = u^2 + 2as \]
Where:
- \( v \) is the final velocity
- \( u \) is the initial velocity
- \( a \) is the acceleration due to gravity
- \( s \) is the distance fallen
Plugging in the values, we get:
\[ v^2 = 0 + 2 \times 9.81 \times 152.4 \]
\[ v^2 = 0 + 2986.13 \]
\[ v = \sqrt{2986.13} \]
\[ v ≈ 54.64 \, m/s \]
So, the impact velocity of the ball bearing when it touches the ground is approximately 54.64 m/s.
Now, whether this velocity can hurt a human depends on various factors such as the angle of impact, the part of the body impacted, the health and condition of the individual, and the material of the ball bearing. Generally, a ball bearing traveling at this velocity has the potential to cause injury, especially if it strikes a vulnerable area such as the head or neck. In some cases, it could lead to major casualties, particularly if the impact causes severe trauma or internal injuries.
It's important to handle objects falling from heights with caution and to take appropriate safety measures to minimize the risk of injury.
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