A) 
The total energy of the system is equal to the maximum elastic potential energy, that is achieved when the displacement is equal to the amplitude (x=A):
(1)
where k is the spring constant.
The total energy, which is conserved, at any other point of the motion is the sum of elastic potential energy and kinetic energy:
(2)
where x is the displacement, m the mass, and v the speed.
We want to know the displacement x at which the elastic potential energy is 1/3 of the kinetic energy:

Using (2) we can rewrite this as

And using (1), we find

Substituting
into the last equation, we find the value of x:

B) 
In this case, the kinetic energy is 1/10 of the total energy:

Since we have

we can write

And so we find:

First we gotta use an equation of motion:

Our vertical distance d= 100 m, initial vertical speed u = 0 m/s (because velocity is fully horizontal), and vertical acceleration a = 9.8 m/s2 because of gravity. Let's plug it all in!

Now we just need to solve for t:

Hit the calculators, and you'll get 4.5 seconds!
Answer:
2.2 s
Explanation:
Hi!
Let's consider the origin of the coordinate system at the ground, and consider that the clam starts with zero velocity, the equation of motion of the clam is given by

We are looking for a time t for which x(t) = 0

Solving for t:

Rounding at the first decimal:
t = 2.2 s
Total momentum after the collision: +200 kg m/s to the right
Explanation:
We can answer this question by using the law of conservation of momentum, which states that for an isolated system (=no external forces acting on the system), the total momentum is conserved.
Mathematically,

where
is the total momentum before the collision
is the total momentum after the collision
In this problem, the system consists of two hockey players. Before the collision, their total momentum is
(to the right)
Therefore, according to the law of conservation of momentum, their total momentum after the collision must be the same:

And given that the sign is +, the direction is still the same, therefore to the right.
Learn more about momentum:
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