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Two highways intersect, as shown in Fig. At the instant shown, a police car P is 41 m from the intersection and moving at 76 km/h. Motorist M is 57 m from the intersection and moving at 62 km/h. At this moment, what is the velocity (magnitude and angle with the line of sight) of the motorist with respect to the police car?

Two highways intersect, as shown in Fig. At the instant shown, a police car P is 41 m from the intersection and moving at 76 km/h. Motorist M is 57 m from the intersection and moving at 62 km/h. At this moment, what is the velocity (magnitude and angle with the line of sight) of the motorist with respect to the police car?

Grade:11

1 Answers

Kevin Nash
askIITians Faculty 332 Points
8 years ago
Assume that the unit vector \widehat{i}points in the positive x direction and the unit vector \widehat{j}points in the positive y direction as shown in figure above.
The velocity of the Police car with respect to ground is:
234-856_1.PNG
The negative sign highlights the fact that the police car moves in a direction opposite to that of unit vector \widehat{i}.
Similarly, the velocity of the motorcyclist with respect to ground is:
234-1551_1.PNG
The negative sign highlights the fact that the motorcyclist moves in a direction opposite to that of unit vector \widehat{j}.
The velocity of the motorcyclist with respect to police car is given as:

234-660_1.PNG
Round off to two significant figures,
234-1999_1.PNG
Therefore, the magnitude of velocity of motorcyclist with respect to police car is 98 km/h .
234-2307_1.PNG
Round off to two significant figures,
θ = - 39°234-1278_1.PNG
Here, L is the separation between the motorcyclist and the intersection point whereas H is the separation between the police car and intersection point (refer figure).
234-1304_1.PNG
Round off to two significant figures,
234-595_1.PNG

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