February 2024
Problem of the Month

Washington Monument Baseball Problem

If a baseball were dropped from the top of the Washington Monument, how fast in miles per hour would it be traveling when it hit the ground?

The Washington Monument is 555 feet tall.

You may use 32 feet per second squared as the acceleration of gravity.

Click here for a story about the first baseballs dropped from the Washington Monument

Solution:

The baseball would be traveling at 128 mph when it hit the ground.

Use the formula for displacement from calculus or physics:
The displacement of an object is equal to the initial velocity multiplied by the time plus half of the acceleration multiplied by the time squared.

Let s = displacement
v₀ = initial velocity
a = acceleration
t = time

s = v₀ t + 1/2 at²

For our problem, v₀ = 0 (it is dropped, so there is no initial velocity), s = 555 feet, and a = 32 ft/s²

555 = (0)t + 16t²
t² = 555/16
t = 5.8896 seconds to hit the ground

Taking the derivative of the displacement with respect to time gives you the velocity:
v = v₀ + at
v = 32 (5.8896) = 188 ft/s

Now use dimensional analysis to change from feet per second to miles per hour.


v = 128 mph

Correctly solved by:

1. K. Sengupta	Calcutta, India
2. Koa Okano	Kalani High School, Honolulu, Hawaii, USA
3. Connor Haapala	Mountain View High School, Mountain View, Wyoming, USA
4. Shyln Schwartz	Mountain View High School, Mountain View, Wyoming, USA
5. Kamal Lohia	Holy Angel School, Hisar, Haryana, India
6. Dr. Hari Kishan	D.N. College, Meerut, Uttar Pradesh, India
7. Kelly Stubblefield	Mobile, Alabama, USA
8. Garrett Short	Mountain View High School, Mountain View, Wyoming, USA

Send any comments or questions to: David Pleacher