a satellite is an orbit 35600km above the surface of the earth. its angular velocity is 7.27*10^-5rad/s. what is the velocity of the satellite (r=6400km)
orbit 35600km above the surface of the earth. its angular velocity is 7.27*10^-5rad/s. what is the velocity of the satellite (r=6400km)
radius from earth center = 3.56 * 10^7 meters + 0.64 * 0^7 meters
= 4.2 * 10^7 meters
v = omega * R = 7.27*10^-5 * 4.2*10^7 = 30.5 *10^2 = 3050 meters/second
if you want km/hr then
3050 meters/second *1 km /1000 m * 3600 s/hr= 11,000 km/hr
ω = v/r
so plug in your numbers
Step-by-step formula and answer
Well, that satellite must be quite the overachiever, spinning around like a champ up there! Now, let's calculate its velocity.
To find the velocity of the satellite, we need to multiply the angular velocity (ω) by its distance from the center of the Earth (r). So, let's plug in the values!
Angular velocity (ω) = 7.27 * 10^-5 rad/s
Distance from the center of the Earth (r) = 6400 km + 35600 km = 42000 km
Now, converting km to meters, we get r = 42000 km * 1000 m/km = 42,000,000 m
Moving on, we can use the formula:
Velocity (v) = ω * r
Plugging in the values:
v = (7.27 * 10^-5 rad/s) * 42,000,000 m
Calculating this, we get:
v ≈ 3054 m/s
So, the speedy satellite is cruising along at approximately 3054 meters per second!
To find the velocity of the satellite, you can use the formula:
v = r * ω
where:
- v is the velocity of the satellite
- r is the distance between the satellite and the center of the Earth
- ω is the angular velocity of the satellite
Given:
- r = 6400 km (distance between the center of the Earth and the satellite)
- ω = 7.27 * 10^-5 rad/s (angular velocity of the satellite)
Let's substitute the given values into the formula:
v = (6400 km) * (7.27 * 10^-5 rad/s)
First, let's convert the distance from kilometers to meters because the angular velocity is in radians per second:
r = 6400 km = 6400 * 1000 m = 6,400,000 m
Now we can calculate the velocity:
v = (6,400,000 m) * (7.27 * 10^-5 rad/s)
Multiply the values:
v = 464.8 m/s
Therefore, the velocity of the satellite is 464.8 m/s.