Calculus

posted by .

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 than 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?

• Calculus -

If the rope is of length h, and the boat is x away from the dock,

h^2 = 1+x^2
When x=8, h = √65

2h dh/dt = 3x dx/dt
Since dh/dt = -1,

2√65 (-1) = 3*8 dx/dt
dx/dt = -√65/12

Since dx/dt < 0, the boat is approaching the dock at about 0.67 m/s

Similar Questions

1. calculus

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 than the bow of the boat. If the rope is pulled in at a rate of 1 m/s, how fast is the boat approaching …
2. Calculus

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 than the bow of the boat. If the rope is pulled in at a rate of 1.4 m/s, how fast is the boat approaching …
3. calculus

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 than the bow of the boat. If the rope is pulled in at a rate of 1.4 m/s, how fast is the boat approaching …
4. Calculus

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 …
5. Calculus

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 …
6. calculus

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 than the bow of the boat. If the rope is pulled in at a rate of 1 m/s, how fast is the boat approaching …
7. Calculus Practice Problems

A boat is pulled into a dock by a rope attached to the bow (front end) of the boat and passing through a pulley on the dock that is 4 m higher than the bow of the boat. If the rope is pulled in at a rate of 3 m/s, at what speed is …
8. Calculus

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 than the bow of the boat. If the rope is pulled in at a rate of 1m/s,how fast is the boat approaching …
9. calc 1

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 than the bow of the boat. If the rope is pulled in at a rate of 1 m/s, how fast is the boat approaching …
10. Calculus

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 than the bow of the boat. If the rope is pulled in at a rate of 1 m/s, how fast is the boat approaching …

More Similar Questions