How Can Vernie and George Swing Across the River Despite the Wind?

[alevis]

Homework Statement

Vernie (mass of 50.0kg) needs to swing across a river to rescue George (mass of 80kg). She must swing into a constant horizontal wind force F ona vine that is initially at an angle of O with the verticle. The width of the river between them is 50.0m. The force of the wind blowing towards Vernie is 110N, and the length of the rope os 40.0m an dthe angle is 50 degrees.
(a.)With what minimum speed must Venie begin her swing in order to just make to the other side.
(b.) Once the rescue is complete, George and Vernie must swing back across the river, with what minimum speed must they begin their swing?


2. L-(Lcos50 deg)
KE(Kinetic Energy)=1/2mv²
PE(Potential Energy)=mgh

The Attempt at a Solution

KE=PE
1/2mv²=mgh

V= sqrt 2gh

 

[Doc Al]

A diagram would be helpful. (Where is the vine with respect to the river?)

In setting up your energy balance equation, don't forget to include the work that must be done against the wind force.

 

[thomate1]

(a.) In order for Vernie to make it to the other side of the river, she must have enough kinetic energy to overcome the gravitational potential energy and the wind force. Therefore, the minimum speed she must begin her swing with can be calculated using the equation V=sqrt(2gh+FdcosO), where g is the gravitational acceleration (9.8 m/s^2), h is the height of the swing (40.0m), F is the wind force (110N), d is the distance across the river (50.0m), and O is the initial angle (50 degrees). Plugging in these values, we get V=sqrt(2(9.8)(40.0)+110(50.0)cos(50))=16.8 m/s.

(b.) Once the rescue is complete and both Vernie and George are on the other side of the river, they must swing back across to the original side. In this case, the minimum speed they must begin their swing with can be calculated using the same equation as before, but with the wind force acting in the opposite direction. Thus, V=sqrt(2(9.8)(40.0)-110(50.0)cos(50))=15.1 m/s. This is the minimum speed for both of them to make it back across the river safely.