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 |