This is a classic example of conservation of energy. Assuming that there are no losses due to friction with air we'll proceed by saying that the total energy mus be conserved.
Now having information on the speed at the lowest point we can say that the energy of the system at this point is purely kinetic:
Where m is the mass of the pendulum. Because of conservation of energy, the total energy at maximum height won't change, but at this point the energy will be purely potential energy instead.
This is the part where we exploit the Energy's conservation, I'm really insisting on this fact right here but it's very very important, The totam energy Em was
It hasn't changed! So inserting this into the equation relating the total energy at the highest point we'll have:
Solving for h gives us:
It doesn't depend on mass!
Speed and direction are the two scientific componets that make up velocity.
Answer
(C).
When there is an angle between the two directions, the cosine of the angle must be considered.
Step by step Solution
The work done by a force is defined as the product of the force and the distance traveled in the direction of motion.
The first answer "Only the component of the force perpendicular to the motion is used to calculate the work" is wrong because, the force perpendicular to motion does no work.
The second choice "If the force acts in the same direction as the motion, then no work is done" is wrong because the work in the direction of the force is 
.
Fourth answer "A force at a right angle to the motion requires the use of the sine of the angle" is wrong because the 
meaning that there is no work done in the direction perpendicular to the motion.
The third answer" When there is an angle between the two directions, the cosine of the angle must be considered." is correct because the work is calculated using the force in the direction of the motion. The magnitude of this force is 
Sure. The acceleration may be decreasing, but as long as it stays
in the same direction as the velocity, the velocity increases.
I think you meant to ask whether the body can have increasing velocity
with negative acceleration. That answer isn't simple either.
If the body's velocity is in the positive direction, then positive acceleration
means speeding up, and negative acceleration means slowing down.
BUT ... If the body's velocity is in the negative direction, then positive
acceleration means slowing down, and negative acceleration means
speeding up.
I know that's confusing.
-- Take a piece of scratch paper, write a 'plus' sign at one edge and
a 'minus' sign at the other edge. Those are the definitions of which
direction is positive and which direction is negative.
-- Then sketch some cars ... one traveling in the positive direction, and
one driving in the negative direction. Those are the directions of the
velocities.
-- Now, one car at a time:
. . . . . first push on the back of the car, in the direction it's moving;.
. . . . . then push on the front of the car, against its motion.
Each push causes the car to accelerate in the direction of the push.
When you see it on paper, all the positive and negative velocities
and accelerations will come clear for you.
