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Question 1194686: You are stationed at a port on the ocean. A cruise liner is sailing past your port. When it goes past you, it is traveling at a speed 30 ft/sec and is 2000 feet from shore.
A. How far will the cruise liner be from you 20 seconds from now?
THIS IS MY ATTEMPT:
30 20=600
X= 2000^2+600^2
x=4,000,000 + 360,000 square root symbol
x=4,360,000square root symbol
=2088.06 ft/sec
B.Once the boat is 2500 ft away from the port, it is no, longer your responsibility to track it. Will the boat be 2500 ft away after 2 minutes?
MY ANSWER:
2502.88 YES THE BOAT IS FAR ENOUGH AWAY.
C. A second boat passes by your port, at a distance of 1500 feet from shore. 10 seconds later, the boat is 2000 ft away from you. How fast was the boat going?
THIS DOESN'T MAKE SENSE TO ME.
Could you please check my work, I don't think I completely understand what the info & questions say. I also think I am missing some formulas for rate/time/ distance. But I don't know.
I am stuck. Sorry I couldn't get the equations to copy and paste correctly. Please help, thank you
Answer by math_tutor2020(3816)   (Show Source):
You can put this solution on YOUR website!
Part A
Let's say the boat is 2000 ft directly north of your location when it passes by.
I'll also have the boat moving east (i.e. to the right).
After 20 seconds, the boat moves d = r*t = 30*20 = 600 ft east.
Your drawing would be of a right triangle with these sides
a = 2000 = vertical leg
b = 600 = horizontal leg
c = unknown hypotenuse
The 90 degree angle is north of your location.
Use the pythagorean theorem to find c.
You have the correct steps and almost the correct final answer.
The units won't be "feet per second" because your teacher is asking about a distance, and not a speed.
Answer: Approximately 2088.06 feet
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Part B
1 minute = 60 seconds
2*1 minute = 2*60 seconds
2 minutes = 120 seconds
Rewind the clock and place the boat directly 2000 ft north of your location again.
After 120 seconds, the boat moves d = r*t = 30*120 = 3600 ft
Recalculate the hypotenuse c
a = 2000
b = 3600
The boat is roughly 4118.25 ft away from your position after 2 minutes.
This exceeds the 2500 ft requirement, meaning that the boat is out of your jurisdiction at this point.
I don't know how you got the 2502.88, but the portion "yes the boat is too far away" is correct.
Answer: The boat is further than 2500 ft at the two minute mark. The boat is no longer your responsibility to track.
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Part C
Let's say the second boat is also going east.
This boat is 1500 ft away from you when it is directly north of your position.
Ten seconds later, it is 2000 ft away from you.
The figure of 2000 ft is the hypotenuse of the right triangle.
The horizontal leg b is unknown
The vertical leg of the triangle is a = 1500 ft
Solve for b using the pythagorean theorem
 approximately
The boat has traveled about 1,322.8756555323 ft in 10 seconds.
distance = speed*time
speed = distance/time
speed = 1322.8756555323/10
speed = 132.28756555323
Answer: The second boat is going about 132.29 ft per second
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Side notes:- I appreciate you showing your work. It's quite rare a student does that on this site.
- Boat speeds are usually measured in knots, aka nautical miles per hour. A nautical mile is not the same as a statute mile (aka land based mile, aka the typical mile many people might think about)
- 1 statute mile = 5280 ft
- There are about 6076 feet in a nautical mile
- A speed of 132.29 ft/s is roughly 78.38 knots, and that is equivalent to about 90.198 mph
- Regardless of the standard of using knots for ocean settings, it's best to stick to the context of the math textbook.
- You can use the notation sqrt to indicate a square root. Example: sqrt(20) =
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