Good morning.
Lets make the movement function for the dog and cat.
The cat has a start position of
1.5 m(the middle of the room), with an initial speed of
0 and acceleration of
0.85 m/s².
The dog has a start position of
0, an initial speed of
1.5 m/s and acceleration of
-0.1 m/s².
<u>Cat:</u>

<u>Dog:</u>

Let's see if the dog reach the cat. Physically, it means


Now we solve for <em>t</em>:

We have a negative Delta.
Therefore, there is no instant t when the dog reaches the cat.
Answer: Hence, ( 30,20 ) will not maximize the profit as it lies inside the solution region.
Explanation:
Answer:

Explanation:
An object is at rest along a slope if the net force acting on it is zero. The equation of the forces along the direction parallel to the slope is:
(1)
where
is the component of the weight parallel to the slope, with m being the mass of the object, g the acceleration of gravity,
the angle of the slope
is the frictional force, with
being the coefficient of friction and R the normal reaction of the incline
The equation of the forces along the direction perpendicular to the slope is

where
R is the normal reaction
is the component of the weight perpendicular to the slope
Solving for R,

And substituting into (1)

Re-arranging the equation,

This the condition at which the equilibrium holds: when the tangent of the angle becomes larger than the value of
, the force of friction is no longer able to balance the component of the weight parallel to the slope, and so the object starts sliding down.