Question

why should pulleys be moving freely?
A FISHING BOAT has a maximum speed of 3 m/s in still water. it is in a river that is flowing at 2 m/s.what can be the max and mini speed of the boat with respect to the river bank?

Answer 1

QUESTION:

1. why should pulleys be moving freely?

2. A FISHING BOAT has a maximum speed of $3\mathrm{m/s}$ in still water. it is in a river that is flowing at $2\mathrm{m/s}$. what can be the max and mini speed of the boat with respect to the river bank?

SOLUTION

Pulleys should be moving freely, because a movable pulley has a mechanical advantage of two, and single fixed pulley hasn't a mechanical advantage, it only changes the direction of force on a rope.

Pic 1. Movable pulley

Pic 2. Fixed pulley

2. According to the Galilean addition of velocities, maximum speed of the boat with respect to the river bank is

$\upsilon_{\mathrm{max}} = 3 + 2 = 5 \mathrm{~m} / \mathrm{s}$, when the boat moves downstream.

Minimum speed of the boat with respect to the river bank is

$\upsilon_{\min} = 3 - 2 = 1 \mathrm{~m} / \mathrm{s}$ when the boat moves upstream.

ANSWER

2. $\upsilon_{\max} = 5 \mathrm{~m} / \mathrm{s}$

$\upsilon_{\min} = 1 \mathrm{~m} / \mathrm{s}$