First, let's remember what it means to have  mole of an atom given its atomic mass unit in Daltons.  mole of oxygen with atomic mass of  is going to be  grams. In kilograms, this would be:

Plugging this into the equation for kinetic energy 

, where  is the mass,  is its velocity. 

For this problem,  and 

Therefore,

Just before impact, the block has maximum kinetic energy. Once the kinetic energy is determined, we can find the potential energy and therefore the height of the drop. We can use the following formula to determine the kinetic energy:

All of this energy was previously potential energy from which we can determine the height, .

We need to know the final speed of the ball since we have all but this quantity in our formula for kinetic energy, 

To find the final velocity we first find the acceleration: 

We can find the final velocity by multiplying the acceleration by the time. We then plug this into the formula for kinetic energy and solve. Do not forget to convert grams to kilograms.

The initial velocity of the cork was zero.

The potential energy stored in a spring is given by

So the energy increases with the square of the compression. When the potential energy is converted to kinetic energy of the cart, it increases by a factor of .

The potential energy stored in a spring is given by

So doubling the compression increases the potential energy by a factor of .  However, the kinetic energy:

, increases with the square of the velocity, so the velocity only needs to double to increase the cart's kinetic energy by a factor of .

Kinetic energy is given by:

, so the energy is linearly dependent on the mass, but increases with the square of the velocity. So although the mass has doubled, the velocity only needs to decrease by a factor of  to maintain the same kinetic energy. In algebraic form:

Simplify.

The equation for kinetic energy is:

Where  is the mass of an object and  is the velocity of the object.

We see from the equation that mass has a linear relationship with kinetic energy and the problem statement gives that the vehicles have the same velocity. Because the car has half the mass of the truck and the same speed, the car has half as much kinetic energy as the truck.

Without specific numbers given, we can always substitute easy numbers into the equation to help understand the concept. If we say the velocity in both cases is , and the car's mass is  then we have:

We know the truck's mass is double the car's, which yields:

This makes it clear that the car has half the kinetic energy of the truck.

There will be two types on kinetic energy, rotational and translational.

Using conservation of energy:

Initially, kinetic energy will be zero, and in the final state, potential energy will be zero.

Recall:

and

Combine equations:

Solve for

Plug in values:

To solve this question, we simply plug in given values into the equation for kinetic energy: