Acar moving at 10 m/s approaches a hill. if the car were put in neutral, it would roll up the hill to a stop at a certain elevation. if the car were approaching the hill instead at 20 m/s, would it roll to stop at the same elevation? you may ignore the effects of friction in your calculations.

They will not stop at same elevation

for v=10m/2 => h=5.1m

for v=20m/2 => h=20.4m

Explanation:

If we neglect the effects of friction in the calculations the energy if the system must be conserved. The car energy can be described as a combination of kinetic energy and potential energy:

The potential energy is due to the gravitational forces and can be describes as:

Where g is the gravitation acceleration, m the mass of the car, and h the elevation. This elevation is a relative quantity and any point of reference will do the work, in this case we will consider the base of the hill as h=0.

The kinetic energy is related to the velocity of the car as:

As the energy must be constant E will be always constant, replacing the expressions for kinetic and potenctial energy:

In the base of the hill we have h=0:

When the car stops moving we have v=0:

This two must be equal:

solving for h:

Lets solve for the two cases:

for v=10m/2 => h=5.1m

for v=20m/2 => h=20.4m

As you can see, when the velocity is the double the height it reaches goes to four times the former one.

answer: the correct answer is 1.

explanation: there are various process in which a radioactive nuclei decays:

1) alpha decay: in this process, a heavier nuclei decays into lighter nuclei by releasing alpha particle. the mass number is reduced by 4 units.

2) electron capture: in this decay process, a parent nuclei absorbs an electron and gets converted into a neutron. simply, a proton and an electron combines together to form a neutron. mass number does not change in this process.

3) gamma ray emission: it is a decay process in which an unstable nuclei gives excess energy by a spontaneous electromagnetic process. this decay releases . this process does not change the mass number.

4) positron emission: it is a type of decay process, in which a proton gets converted to neutron and an electron neutrino. this is also known as -decay. in this the mass number remains same.

from the above information, we see that only alpha-decay is producing a change in the mass number of the nucleus.

statement #3 on andre"s list is false.