Question

A car and a computer monitor are dropped from the top of a cliff. Which one hits the ground first? Why?

Answer 1

As long as air resistance is not an issue, they will hit the ground at the same time. This is because the acceleration due to gravity and the displacement is the same for both objects. The equation to prove this is:

`d = v_"i""t + (1)/(2)at^2`, where `d` is displacement, `v_"i"` is the initial velocity, `t` is time interval, and `a` is acceleration.

Both the computer monitor and car have an initial velocity of 0, so `v_"i""t` = 0, and the equation becomes `d = (1)/(2)at^2`.

Since both the computer monitor and the car have the same displacement and acceleration, the time interval will be the same for both.

`t = sqrt ((2d)/(a)`

Notice that mass is not a variable in this equation. That means that mass is not a factor in determining when the monitor and car will hit the ground. Air resistance can be a factor depending on the shape of the objects, but not their masses.

Consider also the case where you dropped a car and a sheet of paper. You know that the paper will flutter down slowly while the car will drop like a rock. So you might ask yourself if a computer monitor falls more like a car or more like a sheet of paper. The forces acting on a falling object are both gravity and air resistance. A simple description of air resistance can be written mathematically as:
`F = mg - Av^2`
Here `v` is the velocity and `A` is constant describing the geometry of the object and the fluid through which it is falling.

Since the question didn't give us any detailed information about air resistance of the two objects, it's probably safe to assume that air resistance will have very little influence the speed at which they fall. It's probably good enough to say that both will hit the ground at the same time. A very careful measurement may show that one or both fall a little slower than just the force of gravity would predict.

The science of air flow is very complicated. Some good theoretical simulations now exist. The question has been well resolved for simple objects like spheres. For a complex object like a car or computer monitor, it might tumble and the air resistance would depend on which direction it is facing at any moment. The only really good way to determine the answer is to do the experiment. You may need to do it several times with different types of cars and monitors. Each time you will probably want to compare your result with the theoretical `d = (1)/(2)at^2` value.