Answer:

Explanation:
In this case mechanical energy is conserved, which means that the sum of the initial kinetic energy and initial potential gravitational energy will be equal to the sum of the final kinetic energy and final potential gravitational energy:

Which in our case will be:

Which, since
,
,
,
and canceling <em>m</em> means that:

Solving for the final velocity we get:

Personality theorists often focus on differences in individuals.
Answer: Option A
<u>Explanation:
</u>
According to the personality psychology, personality scientists study personality and its variations amongst the individuals. They often focus on the thoughts, judgements and social behaviour of the individuals that they exhibit over time. With these observations, they form a report which better conclude their mental and emotional state.
By studying different types of personalities and respective behaviour, personality theorists are able to predict the diversity in human nature and that whether a person is mentally and emotionally healthy. If not, theorists conduct therapies to get them in order and hence, lead a more meaningful and healthy life.
The correct answer is <span>outboard. This is the most basic type of engine seen everywhere that is attached to regular boats so that you can move them with an engine instead of by rowing. The engine contains all that it needs in the single box and it just gets attached to the boat.</span>
<u>If the disk turns with constant angular velocity, the following statements about it are true
</u>
- The linear acceleration of Q is twice as great as the linear acceleration of P
- is moving twice Q as fast as P.
Answer: Options D and E
<u>Explanation:
</u>
Let us consider that R is the radius of the circular disc. So as Q is on the rim, so the distance of Q from the centre of the disc is R and as P is the midpoint between centre and rim of the disk, so the distance of P from the centre is R/2.
As we know that the angular velocity of the circular disk will be equal to the ratio of distance covered by that point to the time taken. So the angular velocity at point Q will be

As R is the distance of point Q from the centre of the disc.
Similarly
,

So if we equate v with v’ we obtain that

Therefore, the point Q will be moving twice as fast as P. As the velocity of Q is more than O, the linear acceleration of point Q will also be twice as great as the linear acceleration of P.
This is because acceleration is directly proportional to the rate of change in velocity. So if velocity increases in the factor of 2, the acceleration of point Q will also increase twice with respect to point P.
Answer:
65 N
Explanation:
ΣForces = (mass)(acceleration) = all other forces being enacted
The force that the rope exerts is just the tension in the rope caused by the bucket being lifted. I'll take up to be positive and down to be negative, so the tension is an upward force vector and the bucket weight is a downward force vector. By taking into account all the forces involved here, we get the formula:
ΣForces=ma=Tension-mg
- m is the bucket mass
- g is gravity pulling down on the bucket, I'm also taking gravity as 10m/s²
- a is the upward acceleration of the bucket
By isolating Tension we get Tension=ma+mg
Tension = m(a+g)
Tension = 5kg(3+10)m/s²
Tension = (5)(13)N
Tension = 65N