Final answer:
Hitting something at 60 mph is equivalent to falling from approximately a 38-story building.
Step-by-step explanation:
When an object falls, its potential energy is converted into kinetic energy. The speed at which the object hits the ground depends on its initial potential energy, which is determined by its height above the ground.
In this scenario, hitting something at 60 mph is equivalent to falling from a height that would give an object the same kinetic energy when it hits the ground. To determine the equivalent height, we can use the principle of conservation of energy, which states that the total energy of a system remains constant.
Assuming negligible air resistance, the potential energy of the object at its initial height is equal to its kinetic energy when it hits the ground. Using the formula for kinetic energy (KE = 0.5 * mass * velocity^2) and the fact that the object is traveling at 60 mph (which is approximately 27 m/s), we can set the potential energy (PE) equal to the kinetic energy:
PE = KE
m * g * h = 0.5 * m * v^2
Here, 'm' represents the mass of the object, 'g' represents the acceleration due to gravity, 'h' represents the height of the fall, and 'v' represents the velocity of the object.
Cancelling out the mass and rearranging the equation, we get:
h = v^2 / (2 * g)
Substituting the given values for velocity (27 m/s) and the acceleration due to gravity on Earth (9.8 m/s^2), we can calculate the equivalent height:
h = (27^2) / (2 * 9.8)
h ≈ 37.85 meters
Therefore, hitting something at 60 mph is equivalent to falling off of a approximately 38-story building.