A radar antenna is tracking a satellite orbiting the earth. At a certain time, the radar screen shows the satellite to be 159km away. The radar antenna is pointing upward at an angle of 59.3 from the ground.Fine the x and y components(in km) of the position of the satellite
First of all this is not a relative velocity problem -- it is a vector problem.
We'll start by calling the 159km distance R. Since we know the angle of R is 59.3 degrees above the x-axis and R's magnitude is 159 we can solve for the components. Look in your text or notes. To solve for the x component you need to know the equation the x component of R = R*cos(theta) -- or Rx = 159*cos(59.3)
Solving for y is similar. Ry = R*sin(theta) or Ry = 159*sin(59.3)
To find the x and y components of the position of the satellite, we can use the following equations:
For the x component (Rx):
Rx = R * cos(theta)
For the y component (Ry):
Ry = R * sin(theta)
Given that the distance R is 159 km and the angle theta is 59.3 degrees, we can plug in these values into the equations to calculate the components.
Calculating the x component (Rx):
Rx = 159 km * cos(59.3 degrees)
Rx ≈ 159 km * 0.536
Rx ≈ 85.284 km
The x component of the position of the satellite is approximately 85.284 km.
Calculating the y component (Ry):
Ry = 159 km * sin(59.3 degrees)
Ry ≈ 159 km * 0.844
Ry ≈ 134.196 km
The y component of the position of the satellite is approximately 134.196 km.
Therefore, the x and y components of the position of the satellite are approximately 85.284 km and 134.196 km respectively.