Solving a Basic Gravity Problem: How Fast Does a Tomato Fall from 100 Feet?

[TG3]

I feel like an idiot asking this, it's review of a previous course as we start a new quarter, and I KNOW I used to be able to do this... but I don't remember how too. Time to review...

Homework Statement

A tomato is dropped from 100 feet above the ground. At what speed does it hit the ground?
How long does it take to fall the last 100 feet?

Homework Equations

Acceleration due to gravity is 32 ft/sec^2

The Attempt at a Solution

If I recall correctly, delta X = 1/2 at^2
100 = 1/2 32 T^2
200 = 32 T^2
6.25 = T^2
T = 2.5
Tomato hits ground after 2.5 seconds.
So now, plugging that in:
32 (2.5)^2 = 200... which is definitely not right.

 

[LowlyPion]

I feel like an idiot asking this, it's review of a previous course as we start a new quarter, and I KNOW I used to be able to do this... but I don't remember how too. Time to review...

Homework Statement

A tomato is dropped from 100 feet above the ground. At what speed does it hit the ground?
How long does it take to fall the last 100 feet?

Homework Equations

Acceleration due to gravity is 32 ft/sec^2

The Attempt at a Solution

If I recall correctly, delta X = 1/2 at^2
100 = 1/2 32 T^2
200 = 32 T^2
6.25 = T^2
T = 2.5
Tomato hits ground after 2.5 seconds.
So now, plugging that in:
32 (2.5)^2 = 200... which is definitely not right.

Doing it your way, the last step would be V = a*t not t²

Otherwise you could take the Potential energy to kinetic energy relationship:

m*g*h = 1/2*m*V²

or

V² = 2*g*h

 

[nlightner]

As a scientist, it is completely normal to forget certain equations or concepts from previous courses, especially if they have not been used in a while. It is always a good idea to review and refresh our knowledge before starting a new quarter or project. In this case, the equation you are using is correct, but you may have made a mistake in your calculations. The correct answer for the time it takes the tomato to fall from 100 feet is actually 4.47 seconds, and the speed at impact is approximately 64 ft/sec. Make sure to double check your calculations and review the units you are using. It is also helpful to write out all the steps to ensure accuracy. Keep up the good work in reviewing and refreshing your knowledge!