To teach you how to find the parameters characterizing an object in a circular orbit around a much heavier body like the earth.
the motivation for isaac newton to discover his laws of motion was to explain the properties of planetary orbits that were observed by tycho brahe and analyzed by johannes kepler. a good starting point for understanding this (as well as the speed of the space shuttle and the height of geostationary satellites) is the simplest orbit--a circular one. this problem concerns the properties of circular orbits for a satellite orbiting a planet of mass m.

for all parts of this problem, where appropriate, use g for the universal gravitational constant.

a. find the orbital speed v for a satellite in a circular orbit of radius r. (express the orbital speed in terms of g, m, and r),
b. find the kinetric energy k of a satellite with mass m in a circular orbit with radius r. (express your answer in terms of m, m, g, and r).
c. find the orbital period t. (express your answer in terms of g, m, r, and pi).
d. find l, the magnitude of the angular momentum of the satellite with respect to the center of the planet. (express your answer in terms of m, m, g, and r.
e. the quantities v, k, u, and l all represent physical quantities characterizeing the orbit that depend on radius r. indicate the exponent (power) of the radial dependence of the absolute value of each. (express your answer as a comma-separated list of exponents corresponding to v, k, u, and l, in that order.

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.

air exerts forces on falling objects near earth’s surface.

explanation:

the term 'free falls' refer to object that are falling towards the earth, in a situation in which gravity is the only force acting on the object.

for an object in free fall, the acceleration is constant (g, the gravitational acceleration), and so the velocity of the object constantly increases.

for objects near earth's surface, there is always another force acting on the object: the resistance due to the air. this force is opposed to the direction of fall of the object, and it is proportional to the velocity of the object, so as the object falls down, this force increases up to a point when it balances the force of gravity, and the object continues its motion at constant velocity (called terminal velocity). since in this case gravity is not the only force acting on the object, we are not in a situation of free fall.

see the picture for the vector

the magnitude of the vector by pythagorean theorem

r = √( (-10)^2 + (3)^2 ) = √109

magnitude = √109 units

the direction angle between vector and x-axis is

tan^(-1)(3/10) = 16.699

so the direction is approximately 16.7 degrees north of west