It lacked for NOT calculating the FORCES involved. Here they are: To estimate the impact force of a 5-meter fall from a 90 kg person, we can use the work-energy principle which states that the work done by the impact force is equal to the change in kinetic energy. When a person falls from a height, they gain kinetic energy, which is then absorbed by the impact. The kinetic energy (KE) just before impact is given by: $$ KE = \frac{1}{2} m v^2 $$ Where: - \( m \) is the mass (90 kg in this case), - \( v \) is the velocity at impact. The velocity at impact can be found using the equation for velocity of an object in free fall: $$ v = \sqrt{2gh} $$ Where: - \( g \) is the acceleration due to gravity (approximately \( 9.81 \, m/s^2 \)), - \( h \) is the height of the fall (5 meters). Substituting the values, we get: $$ v = \sqrt{2 \times 9.81 \, m/s^2 \times 5 \, m} $$ $$ v = \sqrt{98.1 \, m^2/s^2} $$ $$ v \approx 9.9 \, m/s $$ Now we can calculate the kinetic energy: $$ KE = \frac{1}{2} \times 90 \, kg \times (9.9 \, m/s)^2 $$ $$ KE = \frac{1}{2} \times 90 \, kg \times 98.01 \, m^2/s^2 $$ $$ KE = 4410.45 \, J $$ The impact force (F) can then be estimated if we know the distance over which the impact force acts (d), which is the distance over which the person's momentum is brought to zero. This distance will depend on many factors, including how the person lands and the nature of the surface they land on. Assuming a certain stopping distance, we can use the formula: $$ F = \frac{KE}{d} $$ For example, if the person comes to a stop over a distance of 0.5 meters, the impact force would be: $$ F = \frac{4410.45 \, J}{0.5 \, m} $$ $$ F = 8820.9 \, N $$ So the impact force would be approximately **8820.9 Newtons** or ***8.8 KN***. Please note that this is a simplified calculation and the actual impact force can vary. For accurate results, especially for safety considerations or engineering applications, a detailed analysis considering all relevant factors would be necessary. Source: Conversation with Bing, 4/30/2024 (1) Impact Force Calculator - Calculate the impact force in a collision. www.gigacalculator.com/calculators/impact-force-calculator.php. (2) Impact Force - The Engineering ToolBox. www.engineeringtoolbox.com/impact-force-d_1780.html. (3) Free Fall Force Calculator Online. calculatorshub.net/physics-calculators/free-fall-force-calculator/. (4) Impact Force Calculator | Calculate Impact Force in Collision .... physicscalc.com/physics/impact-force-calculator/. (5) Impact Energy Calculator | Impact Force. www.omnicalculator.com/physics/impact-energy.
