A boat is pulled into a dock by a rope attached to the bow of the boat and passing through a pulley on the dock that is 1 m higher then the bow of the boat. If the rope is pulled in at a rate of 1 m/s, how fast is the boat approaching the dock when it is 8 m from the dock?
2007-10-25 17:18:03 · 6 answers · asked by kgil25 1 in Cars & Transportation ➔ Boats & Boating
1 m.s no acceleration!
2007-10-25 17:26:19 · answer #1 · answered by Brennen 2 · 0⤊ 1⤋
The rope, the dock, and the boat form a right triangle. When the boat is 8m from the dock, the rope is 8/(squareroot(65)) m long. So the ratio is:
8/(squareroot(65)) = x/1
x = 8/(squareroot(65))
2007-10-25 17:28:36 · answer #2 · answered by Kevin 2 · 0⤊ 1⤋
OK, so when the boat is x m away from the dock the length of the rope is √(x^2 + 1) m. So we have
y = √(x^2 + 1)
dy/dt = -1
dx/dt = ?
dy/dt = dy/dx . dx/dt
So -1 = (1/2) (x^2 + 1)^(-1/2) . (2x) dx/dt
so dx/dt = -1 / [x . (x^2+1)^(-1/2)]
= -√(x^2+1) / x
So when x is 8 we have dx/dt = -√(65)/8 ≈ -1.008 m/s. So the boat is approaching the dock at approximately 1.008 m/s.
2007-10-25 17:33:15 · answer #3 · answered by Scarlet Manuka 7 · 0⤊ 0⤋
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2016-11-09 12:15:19 · answer #4 · answered by tschannen 4 · 0⤊ 0⤋
The closer it get, the faster it get there.
2007-10-25 17:35:48 · answer #5 · answered by Snaglefritz 7 · 0⤊ 1⤋
i don't know that
2007-10-29 15:39:36 · answer #6 · answered by kiko 3 · 0⤊ 0⤋