Question

If someone who is 5 feet tall uses a potato gun to shoot a potato in the air at 100 feet per second, we can use the function f(x)=-16x^2+100x+5 to calculate how far the potato will be from the ground at any given second (x). Use this information to determine how long it will take the potato to hit the ground.

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Answer 1

Answer:

Step-by-step explanation:

Given the function f(x)=-16x^2+100x+5 to calculate how far the potato will be from the ground at any given second (x), the potato hits the ground when g(x) = 0

The function becomes'

0 =-16x^2+100x+5

-16x^2+100x+5 = 0

multiply through by minus

16x^2-100x-5 = 0

x = 100 ±√100²-4(16(-5))/2(16)

x = 100±√10000+320/32

x = 100±101.59/32

x = 100+101.59/32

x = 202.59/32

x = 6.299 secs

Hence the potato will hit the ground after 6.299secs

Answer 2

The time taken by potato to hit the ground is $6.299$ seconds.

The potato will be from the ground at any given second (x) is given by below function.

             $f(x)=-16x^2+100x+5$

To find the time taken by potato to hit the ground is , equate given function to zero.

            $f(x)=-16x^2+100x+5=0\\\\-16x^2+100x+5=0\\\\x=\frac{-100\pm\sqrt{(100)^{2}+4*16*5 } }{-16*2} \\\\x=\frac{-100\pm101.587 } {-32} \\\\x=6.299,x=-0.049$

Since, time can not be negative.

So that we will consider , $x=6.299 s$

Hence, the time taken by potato to hit the ground is $6.299$ seconds.

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