Man running up a wheeled block.

[peripatein]

Hi,

Homework Statement

A man, whose mass is m, is running up a block of mass M (as shown in the diagram, please see attachment) with constant acceleration. The block is laid on a smooth ground. The man starts running from rest and the time it takes for him to traverse a distance L (across the block) is T.
(a) What is the man's acceleration relative to the block?
(b) As a result of the run, the block is forced to move right with a constant acceleration A (relative to the ground). What are a_x and a_y of the man, relative to the ground (in terms of A)?
(c) Find A.
(d) What's the block's displacement to the right during T?

Homework Equations

The Attempt at a Solution

(a)In the block's frame of reference and choosing a coordinate system which is parallel to the slope:
mgcos(α) = N; F - mgsin(α) = ma, where I chose F to denote the force exerted by the man running; Lcos(α) = 1/2*a*t², which yielded a = 2Lcos(α)/T²
Are these equations correct? I am not sure.
(b) Won't the acceleration of the man now be:
a = [2Lcos(α)/T² - Acos(α)]_x + [N/m - gsin(α) - Asin(α)/m]_y?
I am waiting for feedback on these first two sections before proceeding to the last two. Would truly appreciate some assistance in this.

 

[mfb]

a) L is the running distance of the man, there is no additional cos(α) involved unless you want to consider the horizontal component of the acceleration only.

Forces and gravity are not relevant. Conservation of momentum is.