(a) No, because the mechanical energy is not conserved
Explanation:
The work-energy theorem states that the work done by the engine on the airplane is equal to the gain in kinetic energy of the plane:
(1)
However, this theorem is only valid if there are no non-conservative forces acting on the plane. However, in this case there is air resistance acting on the plane: this means that the work-energy theorem is no longer valid, because the mechanical energy is not conserved.
Therefore, eq. (1) can be rewritten as

which means that the work done by the engine (W) is used partially to increase the kinetic energy of the airplane (
) and part is lost because of the air resistance (
).
(b) 77.8 m/s
First of all, we need to calculate the net force acting on the plane, which is equal to the difference between the thrust force and the air resistance:

Now we can calculate the acceleration of the plane, by using Newton's second law:

where m is the mass of the plane.
Finally, we can calculate the final speed of the plane by using the equation:

where
is the final velocity
is the initial velocity
is the acceleration
is the distance travelled
Solving for v, we find

The sun’s gravitational attraction and the planet’s inertia keeps planets moving is circular orbits.
Explanation:
The planets in the Solar System move around the Sun in a circular orbit. This motion can be explained as a combination of two effects:
1) The gravitational attraction of the Sun. The Sun exerts a force of gravitational attraction on every planet. This force is directed towards the Sun, and its magnitude is

where
G is the gravitational constant
M is the mass of the Sun
m is the mass of the planet
r is the distance between the Sun and the planet
This force acts as centripetal force, continuously "pulling" the planet towards the centre of its circular orbit.
2) The inertia of the planet. In fact, according to Newton's first law, an object in motion at constant velocity will continue moving at its velocity, unless acted upon an external unbalanced force. Therefore, the planet tends to continue its motion in a straight line (tangential to the circular orbit), however it turns in a circle due to the presence of the gravitational attraction of the Sun.
Learn more about gravity:
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The closer you are to the ground the more accurate you'll be. That's why most snipers are in the "prone" position.
Answer:
a. ρ
b. 
Explanation:
a. To find the density of magnetic field given use the gauss law and the equation:
,
,
Ω,
,
, 
ρ
ρ
ρ
ρ
b. The electric field can be find using the equation:




The vertical force exerted on the lawn is 68.8 N downward
Explanation:
The vertical force exerted by the lawnmower on the lawn is equal to the vertical component of the force applied, therefore:

where
F is the magnitude of the force applied
is the angle between the direction of the force and the horizontal
In this problem:
F = 120 N
Substituting,

where the negative sign means the direction of the force is downward.
Learn more about vector components and forces here:
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