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Grade 11Mechanics

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?

Radhika Batra

11 Years agoGrade 11

1 Answer

Kevin Nash

11 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:

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:

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:

Round off to two significant figures,

Therefore, the magnitude of velocity of motorcyclist with respect to police car is 98 km/h .

Round off to two significant figures,
θ = - 39°

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).

Round off to two significant figures,

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