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Can someone help me solve this

Can someone help me solve this-example-1
User Veblock
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1 Answer

7 votes

Answer:

  1. 168.25 ft
  2. 3.125 s

Explanation:

It is almost too easy to let a graphing calculator show you the solution. (See attached)

_____

You may be expected to use some actual algebra (or even calculus) to find the solution.

If you've spent any time with quadratics, you know the vertex of ax²+bx+c is located at x=-b/(2a). Here, that means the time to get to the highest point is ...

... t = -100/(2·(-16)) = 100/32 = 3.125 . . . . seconds

Then the highest point is ...

... h(3.125) = -16·3.125² +100·3.125 +12 = 168.25 . . . . feet

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Or, you can put the equation into vertex form.

... h(t) = -16t² +100t +12

... = -16(t² +6.25t) +12

... = -16(t² +6.25t +3.125²) +12 +16·3.125² . . . . . add the square of half the t coefficient inside parentheses; add the opposite of the same amount outside parentheses

... = -16(t +3.125)² +168.25 . . . . . simplify

This tells us the peak of the travel of the bullet is at 168.25 ft after 3.125 seconds.

Can someone help me solve this-example-1
User Dwarduk
by
8.1k points

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