Hi there!

1.

The period of a pendulum can be calculated using the following equation:

T = period (s)

L = length of string (m)

g = acceleration due to gravity (m/s²)

Plug in the values:

2.

Calculate the period:

Frequency is the reciprocal of the period, so:

**The correct answer is to avoid air resistance**

Satellites are moving in the orbit because of the initial force that was applied through the rockets. Now for the satellites to remain in orbit there should not be any friction. As air resistance is also friction that is provided by air, the satellites are 150KM above the surface to avoid air resistance

**Answer:**

a)

b)

**Explanation:**

Let´s use Doppler effect, in order to calculate the observed frequency by the byciclist. The Doppler effect equation for a general case is given by:

where:

Now let's consider the next cases:

The data provided by the problem is:

The problem don't give us aditional information about the medium, so let's assume the medium is the air, so the speed of sound in air is:

Now, in the first case the observer alone is in motion towards to the source, hence:

Finally, in the second case the observer alone is in motion away from the source, so:

**Answer**:

102900 Joules

**Explanation**:

Assuming the kinetic energy was zero at the moment of release, you can make the following argument to solve the problem:

The potential energy at full height was mgh. We are told that after 70% of the distance, i.e., mg(0.3h) = 44.1kJ. Since potential energy is linear in altitude h, we get get the full potential energy to be 44.1kJ/0.3. The difference between full potential energy and the one after 70% of the way must equal the gained kinetic energy (neglecting stuff like heat due to friction). So,

44.1kJ/0.3 - 44.1kJ = 0.7*44.1kJ/0.3 = 102.9kJ = Ekinetic

The kinetic energy after 70% of the falling distance was 102.9 kJ.