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Finding Overall Speed and Velocity

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Each of parts (b), (c) and (d) requires you to use numerical answers found in earlier parts of the question.

A dragonfly has a flight speed in still air of 4.5ms-1. It is pointed in the direction N - 29 degree - E, but flies in a wind of speed 7.5ms-1 from the direction S- 42 degree - E. Take i to be 1ms-1 due east and j to be 1ms-1 due north. Also, take

vd to be the velocity of the dragonfly in still air,
vw to be the velocity of the wind,
v to be the resultant velocity of the dragonfly.

(a)
Express each of the vectors vd and vw in component form, giving the components correct to four decimal places.

(b)
Hence show that the resultant velocity v of the dragonfly is given in component form approximately by
v = -2.8368 i + 9.5094 j

(c)
By putting v into geometric form, find the overall speed |v| of the dragonfly (in ms-1 correct to one decimal place) and its direction of travel, as a bearing (with the angle in degrees correct to one decimal place).

(d)
Using your answers to parts (b) and (c), find the time taken by the dragonfly to travel one kilometre (in seconds, correct to one decimal place), and the distance west that it travels in this time (correct to the nearest metre)

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Solution Preview

(a).
vd = 4.5 m/s N 29 degree E == 4.5 m/s, at 29 degree towards East from North
=> vd = 4.5(i sin(29) + j cos(29)) = 4.5*( 0.4848i+ 0.8746j)

=> vd = 2.1816i + 3.9358j --Answer

vw = 7.5 m/s from S 42 degree E ...

Solution Summary

Here we solve a problem related to motion of an object (here dragonfly) influenced by the medium (here wind velocity). We estimate wind velocity of dragonfly and displacement in a given time duration.

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