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In unit vector notation, what is the velocity of the motorist with respect to the police car? and what is the angle between the velocity found and the displacement vector from the police car to the motorist
Transcribed Image Text:### A Motorist and a Police Car
Two highways intersect as shown in the figure. At the instant shown, a police car \( P \) is distance \( d_P = 600 \, \text{m} \) from the intersection and moving at speed \( v_P = 75.0 \, \text{km/h} \). Motorist \( M \) is distance \( d_M = 500 \, \text{m} \) from the intersection and moving at speed \( v_M = 55.0 \, \text{km/h} \).
#### Description of Diagram:
- The diagram shows two perpendicular highways crossing each other, forming an intersection.
- A red car, designated as motorist \( M \), is depicted on the vertical highway above the intersection.
- \( M \) is moving downward towards the intersection at a speed of \( v_M = 55.0 \, \text{km/h} \).
- \( M \) is currently \( d_M = 500 \, \text{m} \) away from the intersection.
- A police car, designated as \( P \), is depicted on the horizontal highway to the right of the intersection.
- \( P \) is moving leftward toward the intersection at a speed of \( v_P = 75.0 \, \text{km/h} \).
- \( P \) is currently \( d_P = 600 \, \text{m} \) away from the intersection.
- The intersection itself is the point where both cars' paths would meet if they continue their respective trajectories. The diagram includes axes labeled \( x \) and \( y \), representing the horizontal and vertical directions respectively.
This setup typically helps in analyzing relative motion, interception point calculations, or determining the time it might take for both vehicles to reach the intersection.
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