How long would it take a car to fall 600 feet?

Answer 1

ABOUT 6 SECONDS

We just had a family member pass this way so I was wondering the same thing. If I remember my calculus and physics correctly, all objects fall at the same speed on earth. That is if we ignore the resistance offered by the wind.

All objects on earth fall at an increasing speed of 32 feet per second squared.

If you want to understand a large portion of calculus using a single example, this is a fantastic question to answer for yourself!

We start off with an object changing its position in the world.

How fast, and in which direction, this object is moving is called velocity, or basically speed for most of us.

How fast the speed of this object is changing is called the acceleration, just like in your car.

That is a great simple, and usable, definition of derivative - or rate at which something is changing.

The opposite of a derivative is an integral, and the opposite of deriving is integrating. So let's integrate!

Thankfully we know everything we need to do this problem. As we know from the start of this adventure, the rate at which the earth's gravity accelerates any of us objects is about 32 feet per second squared. For simplicity's sake let's say 10 meters per second squared.

We can't go into the whole process but I'll show it to you.

32

(Earth's gravitational constant.)

*integrate

1/1 * 32X

or just 10X

(X is going to be our seconds.)

*integrate

1/2 * 32X^2

(Or one half of 32 X squared)

Physicists when using this equation use T for time instead of X, and A for acceleration. You'll commonly see

1/2AT^2

Or one half of the gravitational constant of the planet you're on multiplied by seconds squared.

For us that means 1/2 * 32 * T squared or

16T^2

How long does it take for 16T^2 to equal 600meters?

divide both sides by 16

T^2 = 37.5

take the square root of both sides

T = 37.5^.5

Which is to say the time it takes equals the square root of 37.5.

Using mental math we could say

6 X 6 = 36

7 X 7 = 49

so between six or seven seconds, but much closer to six.

Using a calculator, as well as 9.81 instead of 10 meters per second squared for earth's gravitational constant, you get 6.123 seconds. So you can see using 10 allow for simpler mental calculation is still usably accurate.