Question 821081: lighthouse is 10 km northwest of dock. A ship leaves the dock at 9 am and steams west at 12kph. at what time will it be 8 km from the lighthouse
Answer by TimothyLamb(4379)   (Show Source):
You can put this solution on YOUR website! ---
LH:
adj = hyp cos( 45 )
x = 10 cos( 45 )
x = 7.0711
opp = hyp sin( 45 )
y = 10 cos( 45 )
y = 7.0711
LH point: (7.0711, 7.0711)
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ship at 8 km from LH
point = (x, 0)
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distance formula when ship is at 8 km from LH
8 = sqrt( (x - 7.0710678)(x - 7.0710678) + (0 - 7.0710678)(0 - 7.0710678) )
8 = sqrt( (xx - 14.142136x + 50) + 50 )
64 = xx - 14.142136x + 100
xx - 14.142136x + 36
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the above quadratic equation is in standard form, with a=1, b=-14.142136, and c=36
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to solve the quadratic equation, by using the quadratic formula, copy and paste this:
1 -14.142136 36
into this solver: https://sooeet.com/math/quadratic-equation-solver.php
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the two real roots (i.e. the two x-intercepts), of the quadratic are:
x = 10.8127257
x = 3.32941026
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distance: 8 km from LH when 3.33 km from the dock (along the ship's west course)
time = 3.33/12 = 0.2775 * 60 = 16.65 min
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answer:
at 9:17 AM the ship is 8 km from the lighthouse
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