Question: How fast was the arrow moving before it joined the block?
Answer:
The arrow was moving at 15.9 m/s.
Explanation:
The law of conservation of energy says that the kinetic energy of the arrow must be converted into the potential energy of the block and arrow after it they join:

where
is the mass of the arrow,
is the mass of the block,
of the change in height of the block after the collision, and
is the velocity of the arrow before it hit the block.
Solving for the velocity
, we get:

and we put in the numerical values
,



and simplify to get:

The arrow was moving at 15.9 m/s
Answer:
The resultant velocity is 
Explanation:
Apply the law of conservation of momentum

Where
is the mass of the Luxury Liner = 40,000 ton
is the velocity of Luxury Liner = 20 knots due west
mass of freighter = 60,000
is the velocity of freighter = 10 knots due north
Apply the law of conservation of momentum toward the the west direction

So the equation would be

Substituting values

Where
the final velocity due west
Making
the subject


Apply the law of conservation of momentum toward the the north direction

So the equation would be

Where
the final velocity due north
Making
the subject


The resultant velocity is



Answer:

Explanation:
In order to solve this problem, we can do an analysis of the energies involved in the system. Basically the addition of the initial potential energy of the spring and the kinetic energy of the mass should be the same as the addition of the final potential energy of the spring and the kinetic energy of the block. So we get the following equation:

In this case, since the block is moving from rest, the initial kinetic energy is zero. When the block loses contact with the spring, the final potential energy of the spring will be zero, so the equation simplifies to:

The initial potential energy of the spring is given by the equation:

the Kinetic energy of the block is then given by the equation:

so we can now set them both equal to each other, so we get:

This new equation can be simplified if we multiplied both sides of the equation by a 2, so we get:

so now we can solve this for the final velocity, so we get:

In this question a lot of information's are provided. Among the information's provided one information and that is the time of 4 seconds is not required for calculating the answer. Only the other information's are required.
Mass of the block that is sliding = 5.00 kg
Distance for which the block slides = 10 meters/second
Then we already know that
Momentum = Mass * Distance travelled
= (5 * 10) Kg m/s
= 50 kg m/s
So the magnitude of the blocks momentum is 50 kg m/s. The correct option among all the given options is option "b".