6. The figure below shows a bird\'s-eye view of the trajectories of two speedboa

Question

6. The figure below shows a bird's-eye view of the trajectories of two speedboats, A and B, across the flat surface of a lake. At G there is a stationary guard. Relative to the guard, B travels at a constant speed of 20m/s at an angle ,-30. Relative to the guard, A has accelerated from rest at a constant rate of 0.4m/s2 at the angle 600 . At a certain time during the acceleration, A has a speed of 40m/s. At that time, express the velocity of A relative to B in unit vector notation and calculate its magnitude and direction. (b) At the same time, express the acceleration of A relative to B in unit vector notation and calculate its magnitude and direction 0 2

Explanation / Answer

A) Velocity of A with respect B = (40 cos 60 degree i + 40 sin 30 degree j) - (20 cos 30 degree i + 20 sin 60 degree j)

= (40*0.5 - 20*0.866) i + (40*0.866 - 20*0.50) j

= 2.68 i + 24.64 j

Magnitude = 24.8 m/s

Direction = 83.8 degree N of E.

B)magnitude a = 0.4m/s^2

Direction =60 degree

in vector form : 0.4 cos 60 degree i + 0.4 sin 60 degree j

= 0.2 i + 0.364 j m/s^2

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