I need help on Vector Mechanics homework

This homework is about Vector Mechanics. Show clear solution step by step and clear FBD

1.) (50 points) In the figure below, the blocks are released from rest and they have the
following masses:
ma= 35kg, m8 =10kg
The coefficient of kinetic friction between block A and the incline is uk=0.20. The coefficient of
kinetic friction between block A and block B is MK=0.10. (Assume that the system begins moving
when it’s released from rest, and therefore that static friction will not be strong enough to hold
the system at rest.)
B
10
ty
.X
110
A
30°
30°
*Y
a.) Using the outlines provided (on the next page), draw the free-body diagrams for (illustrate
each force acting upon) block A and block B.
b.) Using the free-body diagrams constructed, write all the Newton’s 2nd law equations (an x-
component equation and a y-component equation) for block A and block B using the
“preferred” coordinate systems provided: P for block A and Q for block B. (The equations
should be written on the next page with the corresponding free-body diagram.)
c.) Find the equations that relate the two coordinate systems (their unit vectors), P and Q.
d.) Write the relative motion equation for the acceleration of block B relative to block A.
e.) With all of the equations produced (along with the general equations used to calculate the
magnitude of kinetic friction using the appropriate normal force), set up a matrix and solve
for the value of all the variables (unknowns) present.
f.) Give the acceleration of block A and block B in coordinate system O.
у
30°
Р
А
*y
,
10°
В
2.) (30 points] Car A, initially travelling 120km/h, enters a so-called “hairpin turn” as shown in
the diagram below. Starting at point P, car A begins decreasing its speed at a rate of 2m/s2.
(The mass of both cars is 1,550kg.)
120 km/h
P
.
r = 70 m
40 km/h
Once car A has travelled a distance of 155m around the turn from point P, determine:
a.) car A’s velocity, in the given Cartesian (xy) coordinates, at that time
b.) the net force acting on car A, in the given Cartesian (xy) coordinates, at that time
c.) car B’s velocity relative to car A (assuming car B isn’t accelerating and is still on the straight
section of the road) at that time, in the given Cartesian (xy) coordinates
d.) car B’s acceleration relative to car A (assuming car B isn’t accelerating and is still on the
straight section of the road) at that time, in the given Cartesian (xy) coordinates
3.) (40 points) The parasailing system shown uses a winch to pull the rider in towards the boat.
With Ⓡ = 40° at t = 0, the angle o initially begins decreasing (“from rest”) due to an angular
acceleration of 0.25°/s2. The length of the rope is defined by the relationship
r = 115m – (0.0015m/s2)tº, where r and t are expressed in meters and seconds, respectively.
At t = 0, the boat itself begins decelerating at a rate of 0.35m/s2 from its initial speed of 25m/s.
At the instant shown (below), when 0 = 10°, the person drops their sunglasses.
>+x
o
Determine:
a.) the velocity, relative to the boat, of the person at the instant shown (using the “preferred”
unit vectors for noncircular curved motion)
b.) the velocity, relative to the shore, of the person at the instant shown (using the Cartesian
coordinate system, o, provided above)
c.) the acceleration, relative to the shore, of the person at the instant shown (using the
Cartesian coordinate system, o, provided above)
d.) the impact location, relative to where the rope attaches to the boat, of the sunglasses