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The quadratic equation y = -16t^2 + 4t + 2 represents a moving object's trajectory where y is the object's height in feet above the ground after t seconds. At what time will the object hit the ground?
a.) 2 seconds

b.) 0.25 seconds

c.) 0.5 seconds

d.) 1 second

Sagot :

eliezerkafunya

Answer:

c. o.5seconds

Step-by-step explanation:

y=-16t^2 +4t+2

=-2(8t^2 -2t-1)

=-2(8t^2 -4t+2t-1)

as the object hits the ground y =0

0 =-2(4t+1)(2t-1)

(4t+1)(2t-1)=0

t=-1/4 meangless

t=1/2

=0.5seconds

Answer:

If y is the height of the ball, then y = 0 when the ball is on the ground. Plug 0 in for y and use the quadratic equation to find the solutions:

0 equals short dash 16 t squared plus 4 t plus 2

t equals fraction numerator short dash 4 plus-or-minus square root of 4 squared minus 4 left parenthesis short dash 16 right parenthesis left parenthesis 2 right parenthesis end root over denominator 2 left parenthesis short dash 16 right parenthesis end fraction

t equals fraction numerator short dash 4 plus-or-minus square root of 16 minus open parentheses short dash 128 close parentheses end root over denominator short dash 32 end fraction

t equals fraction numerator short dash 4 plus-or-minus square root of 144 over denominator short dash 32 end fraction

t equals fraction numerator short dash 4 plus-or-minus 12 over denominator short dash 32 end fraction

t equals fraction numerator short dash 4 minus 12 over denominator short dash 32 end fraction space o r space fraction numerator short dash 4 plus 12 over denominator short dash 32 end fraction space

t equals 0.5 space O R space short dash 0.25

Since we are looking for a distance, only the positive answer of 0.5 is appropriate.

so, C. 0.5 seconds

Step-by-step explanation:

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