Polar Coordinates Example 1

The video tutorial explains how to solve a polar coordinates problem involving a plane tracked by radar. It covers setting up equations for the plane's path, finding its position, and determining the velocity vector's angle and components. The solution involves using the polar coordinates formula to calculate the plane's speed.

What is the initial angle theta of the plane from the horizontal as tracked by the radar?

• 150 degrees

• 120 degrees

• 90 degrees

• 180 degrees

What is the equation of the line representing the plane's path?

• y = tan 180x

• y = tan 90x

• y = tan 120x

• y = tan 150x

What is the x-coordinate of the plane's position after solving the quadratic equation?

• -901 meters

• 1479 meters

• 1000 meters

• 500 meters

How is the radial distance 'r' calculated?

• Using the sum of x and y

• Using the difference of x and y

• Using the square root of the difference of x squared and y squared

• Using the square root of the sum of x squared and y squared

What is the gradient of the curve at the point of interest?

• 4.41

• 3.41

• 6.41

• 5.41

What is the angle gamma of the velocity vector from the horizontal?

• 79.5 degrees

• 60 degrees

• 90 degrees

• 70 degrees

What is the angle between the radial and theta components of the velocity vector?

• 30 degrees

• 45 degrees

• 60 degrees

• 90 degrees

What is the formula used to express the velocity vector in polar coordinates?

• r dot er + r theta dot e theta

• r theta dot er + r dot e theta

• r dot e theta + theta dot er

• r er + theta e theta

What is the calculated speed of the plane in meters per second?

• 120.6 m/s

• 138.6 m/s

• 150.6 m/s

• 160.6 m/s

What is the equivalent speed of the plane in kilometers per hour?

• 399 km/h

• 449 km/h

• 499 km/h

• 549 km/h