Speed And Distance - Free Falling Object

**Strings (S _{i}P_{j}A_{jk}) = S_{7}P_{5}A_{51} Base Sequence = 12735 String Sequence = 12735 - 5 - 51 **

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Free Falling Object - Speed Distance Relation

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(a) Given that *v* is the speed at time *t* of an object free falling to earth and *d* is the distance the object has fallen at time *t*. Derive a relation between *v* and *d*.

(b) Using the relation derived in (a), calculate the speed with which an object dropped from the top of a building 1000 ft above street level hits the ground.

**The string**: S_{7}P_{5}A_{51} (speed-physical change); S_{7}P_{4}A_{41} (Linear motion)
**The Math**:

Neglecting air resistance, an object falls to earth with a constant acceleration:
* a = 32 *ft/sec^{2}.

A falling object with an initial velocity of zero, gains speed each second at the rate of 32 ft/sec.

So after t secs, speed v = 32t----(1).

avrage speed is attained after one-half of the time traveled.

So average speed = 32t/2 = 16t----(2)

So distance after t secs, d = average speed x time = 16t^{2}---(3)

From equation (3), t = √(d/16)

substituting this value of t into equation (1),
we have:

v = 8√d----(4)

Expressing equation (4) in terms of d,
we have:

d = v^{2}/64----(5)

To calculate speed of object when it hits the ground use equation (4)

So, v = 8√1000 = 256 ft/sec approximately.

The *point* **.** is a mathematical abstraction. It has negligible size and a great sense of position. Consequently, it is front and center in abstract existential reasoning.

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