Question

8. A boat is being pulled into a wharf by a rope that passes over the edge of the wharf and is attached to the boat at a point which is 8 ft. below the level of the wharf. a) If the rope is being pulled in at a rate of 24 ft/min, how fast is the boat moving when there are 17 ft. of rope still out?

Answer 1

Answer:

the speed of the boat is 21.22ft/min

Explanation:

Hello!

To solve this exercise follow the steps below.

1. Draw the complete scheme of the problem (see attached image).

2. As you can see in the image, our goal is to determine the horizontal component of the velocity (Vx) that corresponds to that of the boat, for this the first thing we do is find the alpha angle using the height and the hypotenuse of the  triangle.

$sin (\alpha )=\frac{8}{17} \\\alpha =sen^-1(\frac{8}{17})=28$

3. Finally we find the horizontal velocity component using the cosine function

$cos(\alpha)=\frac{Vx}{24ft/min} \\Vx=(24ft/min)cos(28)=21.22ft/min$

the speed of the boat is 21.22ft/min