Two toy racecars race along a circular race track. Both cars start at the 3-o'clock position and travel in the CCW direction. Let t represent the number of seconds since the start of the race. Imagine angles with terminal rays that pass through each car as it moves. Car A is constantly 4.5 feet from the center of the race track and travels a constant speed. The angle with a terminal ray passing through Car A sweeps out 2.5 radians per second. Write an expression (in terms of t) that represents Car A's vertical distance above the center of the race track in feet.

On the map, let the +x-axis point east and the +y-axis north. An airplane flies at 880 km/h northwestward direction (i.e., midway between north and west). Can you help me visualize the components of the first velocity, and when the plane flies due south at the same velocity.  I understand the answer will be -622.25 for the run, meaning 880*cos(45) for x -axis; the y axis north is 880*sin(45) resulting in 622.5 Please help me visualize the first and second velocity when the plane flies due south at the same velocity?  Help me to visualize where one of the velocities due south is zero, and the other is whatever it is.   I am afraid I can properly visualize or understand in simple terms what is asked.  My point can you help to understand the right angle theorem to the angle.

Hiker Harry walks 4 km east then 7 km 25o north of west. What is the magnitude and direction of Harry’s position after his hike as measured from his starting point? Give the angle measured relative to east. For example 90° means directly north.

After enjoying a big sandwich at Katz's Delicatessen, you decide to walk back to your luxury suite at the Waldorf-Astoria Hotel. First, you perambulate 0.15 mi at a polar angle of 160 degrees 0.15 mi angle 160^ ) . Next, you skedaddle 1.60 mi at a polar angle of 55 degrees (1.60 mi angle55^ ) . You follow this with a 0.55 mi jaunt at a polar angle of 150 degrees (0.55 mi angle150^ ) Finally, you be-bop 0.82 mi at a polar angle of 60 degrees (0.82 mi angle 60^ ) . What is the overall displacement from your starting point at Katz's Delicatessen? Express your answer in polar notation.