Question

A perfectly frictionless ball is dropped from the Empire State Building observation deck (425 meters above the sidewalk). How fast is the ball traveling when it hits the sidewalk?

a) 9.8 m/s
b) 45 m/s
c) 89 m/s
d) 178 m/s

Answer 1

The ball dropped from the Empire State Building will be traveling approximately 91.27 m/s when it hits the sidewalk, making the closest answer choice 89 m/s (option c).

Step-by-step explanation:

To determine how fast the ball is traveling when it hits the sidewalk, we can use the equations of motion for an object in free fall due to gravity, ignoring air resistance. The formula relevant in this scenario is:

v = √(2gh)

where v is the final velocity, g is the acceleration due to gravity (9.8 m/s2), and h is the height from which the ball was dropped.

Given that the ball was dropped from 425 meters:

v = √(2 * 9.8 * 425) = √(8330) ≈ 91.27 m/s

The value of 91.27 m/s suggests that the correct answer would be closest to 89 m/s (option c), considering the choices provided assume we're rounding to the nearest whole number.