Trying to understand the solution given

[issacnewton]

Hello, following is the mechanics problem involving pulley from an engineering mechanics book. I am trying to understand the solution given. As the car is being pulled, upward of the incline is assumed to be positive x direction. But when they apply the relative acceleration equation, in eq 3, the acceleration of the point P with respect to the car is entered as +4. Since the acceleration of the point P with respect to the car is acting downward the incline, this should be entered as -4 in equation 3. What people here think ? I have attached the problem and its solution as the PNG image file.

thank you

 

[haruspex]

Read it more carefully. It says the position and acceleration of the car are measured down the plane.

 

[issacnewton]

Hello haruspex, sorry for late reply. But where is the statement which says that position and acceleration are measured down the plane ? If you look at the picture of the axes given in the solution, positive x-axis is point upward the incline...

 

[jtbell]

Look at the direction of the arrows in diagram (b).

 

[haruspex]

Hello haruspex, sorry for late reply. But where is the statement which says that position and acceleration are measured down the plane ? If you look at the picture of the axes given in the solution, positive x-axis is point upward the incline...

Second sentence in the paragraph headed "free body diagram"

 

[issacnewton]

yes, I see now. thanks both of you.