A boat is pulled into a dock by a rope attached to the bow of the boat an passing through the pulley on the deck that is 1m high than the bow of the boat ,if the rope is pulled im at the rate of 0.8m/s how fast does the boat approach the deck when it is 10m from the dock?
To find the speed at which the boat approaches the deck, you can use the concept of related rates. This involves finding the rate at which one quantity changes with respect to another.
Let's define some variables:
H = height of the bow of the boat from the dock
x = horizontal distance between the boat and the dock
From the problem, we know that H = x + 1 (the deck is 1 meter higher than the bow of the boat). Also, we are given that dx/dt (rate of change of x) is 0.8 m/s.
To find dh/dt (rate of change of H) when x = 10 m, we need to differentiate H with respect to time (t) and apply the chain rule:
dh/dt = d/dt (x + 1)
= dx/dt
Substituting the given value, we have:
dh/dt = 0.8 m/s
Therefore, the boat approaches the deck at a speed of 0.8 m/s when it is 10 meters from the dock.