The general formula to calculate the work is:

where F is the force, d is the displacement of the couch, and
is the angle between the direction of the force and the displacement. Let's apply this formula to the different parts of the problem.
(a) Work done by you: in this case, the force applied is parallel to the displacement of the couch, so
and
, therefore the work is just equal to the product between the horizontal force you apply to push the couch and the distance the couch has been moved:

(b) work done by the frictional force: the frictional force has opposite direction to the displacement, therefore
and
. Therefore, we must include a negative sign when we calculate the work done by the frictional force:

(c) The work done by gravity is zero. In fact, gravity (which points downwards) is perpendicular to the displacement of the couch (which is horizontal), therefore
and
: this means
.
(d) Work done by the net force:
The net force is the difference between the horizontal force applied by you and the frictional force:

And the net force is in the same direction of the displacement, so
and
and the work done is

Answer:
(a) 
(b) 
(c) 
Explanation:
(a) According to Newton's second law, the acceleration of a body is directly proportional to the force exerted on it and inversely proportional to it's mass.

(b) According to Newton's third law, the force that the sled exerts on the girl is equal in magnitude but opposite in the direction of the force that the girl exerts on the sled:

(c) Using the kinematics equation:

For the girl, we have
and
. So:

For the sled, we have
. So:

When they meet, the final positions are the same. So, equaling (1) and (2) and solving for t:

Now, we solve (1) for 

Answer:

Explanation:
Given data
Electromagnetic waves from the sun is I=1.4kW/m² at 80%
Area a=(0.30×0.51)m²
Time t=1.30 hr
To find
Energy E
Solution
The energy received by your back is calculated as:

Answer:
7.5s
Explanation:
Given parameters:
Velocity = 30m/s
Deceleration = 4m/s²
Unknown:
Time it takes for the car to come to complete rest = ?
Solution:
To solve this problem, we use the kinematics expression below:
v = u + at
Since this is a deceleration
v = u - at
v is the final velocity
u is the initial velocity
a is the acceleration
t is the time taken
v - u = -at
0 - 30 = -4 x t
-30 = -4t
t = 7.5s