Two "Stationary" or "Synchronous" communications satellites are put into an orbit whose radius is 4.23 ?

Two "Stationary" or "Synchronous" communications satellites are put into an orbit whose radius is 4.23 x 10^4 km. This means the satellites are always at the same location in the sky, relative to an observer on the ground. The orbit is in the equator (all geosynchronous satellite orbits must be), with an angular separation of 2.00 degrees. Find the arc length between the two satellites. (For this and all other questions, choose the closest answer).


2.25 x 10^7 m


861 x 10^9 m


7.39 x 10^8 m


1.48 x 10^6 m





2. A fan with blades 25.4 cm in diameter is rotating at a rate of 1740 rpm. What is the speed of a point at a blade tip?


38.9 m/s


23.2 m/s


44.6 m/s


12.9 m/s





3. If a point on the rim of a wheel 10 cm from the center of the wheel has a linear speed of 20 cm/s, what is the period of revolution of the wheel?


3.14 s


0.824 s


4.66 s


8.32 s

Two "Stationary" or "Synchronous" communications satellites are put into an orbit whose radius is 4.23 ?
#1) Solve the equation 2/360 = x/(2*pi*r) for x to find the arc length between the two satellites:





x = (2*pi*r)/360 = 1.48 x 10^3 km = 1.48 x 10^6 m.





#2) 25.4 cm = 0.254 m


1 rev = 2 * pi * r = 6.28 * 0.127 = 0.798 m


If the fan blade does 1740 rev/min, it travels 1740*0.798 =1389 m/min. Divide by 60 to get m/s:


1389/60 = 23.2 m/s





#3) 1 rev = 0.1*2*pi = 0.628 m


Divide this by the speed in m/s of the rim of the wheel to get how many seconds there are per revolution, which is the period of the wheel:


0.628 / 0.2 = 3.14 s





I hope this helps you!