Calculating the Impact Speed of a Penny Dropped from High Buildings

To accurately determine the speed at which a penny hits the ground when dropped from the top of a skyscraper, we can use the principles of free fall and kinetic equations. This article delves into the physics behind such scenarios, focusing on the Chrysler Building and the Empire State Building, as well as the peculiar behaviors of pennies due to air resistance.

Chrysler Building Example

Consider a penny dropped from the top of the Chrysler Building, which stands at a height of 320 meters. Using the laws of physics, we can calculate the impact velocity of the penny when it hits the ground.

Equation Setup and Calculation

We start with the given parameters:

Height, ( y 318 ) m Initial velocity, ( v_o 0 ) m/s Acceleration due to gravity, ( g 9.8 ) m/s2

The kinematic equations for this scenario are:

y12gt2

vfv0 gt

First, we need to find the time, ( t ), it takes for the penny to reach the ground:

y12gt2318129.8t2t23184.9t64.7t27795

Next, we calculate the final velocity, ( v_f ):

vf0 9.864.7vf-635.1168109#8239;m/svf-78.95#8239;m/s

The negative sign indicates the downward direction. The penny hits the ground at a speed of approximately 78.95 m/s.

Empire State Building Example

The Empire State Building is significantly taller, standing at 320 meters from its observation deck to the ground. Assuming no air resistance, the penny would hit the ground at an estimated speed of 79.3 m/s. However, the air resistance experienced by a penny is substantial, especially during its early descent.

Air Resistance and Terminal Velocity

Due to air resistance, pennies only reach their terminal velocity after a short distance. The terminal velocity of a penny in air is approximately 64.4 mph (28.9 m/s). For the Empire State Building, the air certainly adds an uplifting component, reducing the speed even further.

Despite reaching terminal velocity, a penny's impact is not overly violent at high speeds. It will not break skin or cause bleeding; rather, it will merely sting upon impact.

Conclusion

The impact speed of a penny dropped from a tall building is influenced by air resistance and the building's height. Understanding the physics involved aids in predicting and analyzing such scenarios accurately.

Keywords: penny drop, impact velocity, terminal velocity, free fall, skyscraper