Question

On Myth Busters it was determined that a penny dropped from the top of the Empire State Building would reach a terminal velocity of 64.4 miles per hour before hitting the ground. What is the height of the building in feet needed for a penny with a mass of 2.5 grams to reach a velocity of 46.7 miles per hour? Assume that no energy is lost from frictional drag. For the acceleration of gravity on the Earth us 9.81 meters per second squared or 32.2 feet per second squared.

Answer 1

If the ground level is taken as "zero", reference level for the potential energy.

The potential energy of the penny before being dropped is

where:

m is mass of the penny

g is acceleration due to gravity

h is the height of the building.

and before being dropped, the velocity is zero and hence kinetic energy is also zero.

Hence total initial mechanical energy is

when the penny is about to touch the ground, (it has travelled down the height of the building), the potential energy is zero and the kinetic energy is

hence the net final energy is also

as no frictional drag loss is assumed, the net mechanical energy remains conserved.

Hence

as it can be seen that the mass term is cancelled out from both the sides of the equation, hence the final velocity does not depend on the mass of the object

now , given that we need to achieve the final velocity as

v= 46.7 miles per hour = 20.877 meters per second

g= 9.81m/s^2

putting these values, we get

hence to achieve the value of 46.7 miles per hour velocity, the height of the Empire States building must be 146.26 meters.