Alfi Blog

Alfi Blog

Alfi Blog


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Geometric Problems

Geometric Problems

 

To solve word problems involving geometric shapes, write down the formula or formulas referred to in the problem. For example, after reading ‘‘The perimeter of a rectangular room . . . ’’ write P = 2L + 2W. Then fill in the information given about the formula. For example, after reading ‘‘The peri- meter of the room is 50 feet . . . ’’ write P = 50 and 50 = 2L + 2W. ‘‘Its width is two-thirds its length.’’ Write W = L and 50 = 2L + 2W becomes 50 = 2L + 2( L).

The Height of a Falling Object - 2

Examples

 

An object is tossed up in the air at the rate of 40 feet per second. How long will it take for the object to hit the ground?

The Height of a Falling Object - 1

Example

 

An object is dropped from the roof of a 60-foot building. How longbmust it fall to reach a height of 28 feet?

   In the formula h = 16t2 + v0t + h0, h0 is 60 and v0 is zero (because the object is dropped). The object reaches a height of 28 feet when h = 28.

The Height of a Falling Object

The Height of a Falling Object

 

The height of an object dropped, thrown or fired can be computed using quadratic equations. The general formula is h = 16t2 + v0t + h0, where h is the object’s height (in feet), t is time (in seconds), h0 is the object’s initial height (that is, its height at t = 0 seconds) and v0 is the object’s initial velocity (that is, its speed at t = 0 seconds) in feet per second. If the object is tossed, thrown, or fired upward, v0 is positive. If the object is thrown downward, v0 is negative. If the object is dropped, v0 is zero. The object reaches the ground when h = 0. (The effect of air resistance is ignored.)

Work Problems

 

Work Problems

 

REVIEW

 

Solve work problems by filling in the table below. In the work formula Q = rt (Q = quantity,  r =  rate,  and  t =  time),  Q  is  usually  ‘‘1.’’  Usually the equation to solve is:

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