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 1m higher than the bow of the boat. If the rope is pulled in at a rate of 1m/s, how fast is the boat approaching the dock when it is 8m from the dock?
Solution Summary
This solution shows how to solve the word problem using differentiation in an attached Word document.
A boat is being pulled into a dock with a rope attached to theboat at water level. when theboat is 12 feet from the dock, the length of the rope from theboat to the dock is 3 feet longer than twice the height of the dock above the water.
- Determine the equation needed to find the height of the dock.
- Find the height
2 (a) If A is the area of a circle with radius r and the circle expands as time passes, find dA/dt in terms of dr/dt
(b) Suppose oil spills from a ruptured tanker and spreads in a circular pattern. If the radius of the oil spill increases at a constant rate of 1m/s howfast is the area of the spill increasing when the radius
Relative Velocity Problem
Consider a boat on the West bank of a river of width D=1664 meters to be at the origin of an x,y axis system with the 0° direction East along the +x axis.
The river water runs South with velocity vector W= 3.9 m/sec at 270°.
At coordinates (1200, -390) is a dock on an island. At coordinates (16
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30. A boat is pulled into a dock...
(a) Determine the speed of theboat when there is 13 feet of rope. What happens to the speed of theboat as it gets closer to thedock?
(b) Determine the speed of the rope when there is 13 feet of rope. What happens to the speed of the ro
Joe enjoys fishing & goes out about 20 times per year. One day, Sara told him that fishing is too expensive of a hobby. She thinks he should stop going because she calculated that it costs about %28.75 for every fish he catches because he usually catches about 20 fish per trip. She says it would be much cheaper to buy fish fr
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1.Boat A is sailing south at 24 km/h while boat B, which is 48 kilometres due south of A, is sailing east at 18km/h.
a)At what rate are they approaching or separating one hour later?
b)When do they cease to approach on another and how far apart are they at this time?
c)What
1. Consider a supply chain consisting of a single manufacturing facility, a cross-dock, and two retail outlets. Items are shipped from the manufacturing facility to the cross-dock and from there to the retail outlets. Let L1 be the lead time from the facture to the cross-dock facility and L2 be the lead time from the cross-dock
A child in a boat throws a 6.00 kg package out horizontally with a speed of 10 m/s. Calculate the velocity of theboat immediately after, assuming it was initially at rest. The mass of the child is 24.0 kg and that of theboat is 50.0 kg.
Two people, one of mass 70 kg and the other of mass 60 kg, sit in a rowboat of mass 80 kg. With theboat initially at rest, the two people, who have been sitting at opposite ends of theboat, 3.0 m apart from each other, exchange seats. How far will theboat move?
