Two skiers, Annie and Jack, start skiing from rest at different points on a hill at the sa...

RESEARCH:

The poison vector of the combined center of mass for Annie and Jack is

…… (1)

The velocity vector of the combined center of mass for Annie and Jack is

…… (2)

The acceleration vector of the combined center of mass for Annie and Jack is

…… (3)

SIMPLIFY:

When an object is slides down on an incline plane, the acceleration given by

Acceleration of Annie in axis direction is

Acceleration of Jack in axis direction is

Acceleration of Annie in axis direction is

…… (4)

Acceleration of Jack in axis direction is

…… (5)

Then

…… (6)

…… (7)

Since each skier starts from rest, the initial speeds of both are zero.

From the equation of motion, , since

In axis direction,

…… (8)

And

…… (9)

By substituting the equation (8) and (9), in the equation (2), we get

…… (10)

Similarly,

…… (11)

From the equation of motion,

The position vectors of Annie and Jack are:

In axis direction:

…… (12)

Substitute the value of in the equation (12), we get

…… (13)

From the diagram,

Similarly,

In the axis direction,

…… (14)

And

…… (15)

From the diagram,

From equation (1), (14) and (15), we get

……. (16)

……. (17)

CALCULATE:

Given,

Mass of the Jack is

Steeper section with an angle of inclination of

Mass of the Annie is

Angle of inclination for Annie is

Length of the steeper section is

By substituting all known values in the equations (7) and (8), we get

The component acceleration of the center of mass for Annie and Jack is

The component acceleration of the center of mass for Annie and Jack is

By substituting all known values in the equations (10) and (11), we get

The component velocity of the center of mass for Annie and Jack is

The component velocity of the center of mass for Annie and Jack is

By substituting all known values in the equations (16) and (17), we get

The component poison of the center of mass for Annie and Jack is

The component velocity of the center of mass for Annie and Jack is