Question

The empire state building stands at a height of 1,454 feet. Given the choice between feet feet per second or miles per hour, which rate of measure is more reasonable to describe the speed of a penny when dropped off the top of the building? Justify your reasoning using mathematical laguage

Answer 1

miles per hour

Explanation:

speed can be define as the rate of distance covered in a given time.

i.e speed =
`(distance)/(time)`

Given that the height (distance) of the empire state building = 1454 feet.

a. For feet per second;

distance = 1454 feet

time = 1 second

speed =
`(1454)/(1)`

= 1454 feet/second

b. For miles per hour,

1 feet = 0.000189394 mile

Thus, 1454 feet = 0.2753788 mile

distance = 0.2753788 mile

time = 1 hour

speed =
`(0.2753788)/(1)`

= 0.2753788 miles/hour

Comparing the two units of measurement, miles per hour is more reasonable. This is because the penny can not move at that very high speed to hit the ground within 1 second when dropped.