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.
Express each of the vectors vd and vw in component form, giving the components correct to four decimal places.
Hence show that the resultant velocity v of the dragonfly is given in component form approximately by
v = -2.8368 i + 9.5094 j
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).
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)
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 ...
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.
Frequency and angular frequency, rotations per second.
Saw on internet some equations to convert from frequency in hertz to mph. Some equations need a gear ratio while others do not. I found the equation mph = circumference * RPM * 60. Now, it makes sense and if use dimensional analysis I found 1Hz = 60 RPM and 60Hz = 3600 RPM. When calculated for a diameter of a motor shaft with a blade of 30 inches the mph for 1 hz and up to 60Hz is huge. Not at what I see the blade turn at. I got for 60Hz 339,120 inches/sec and 28,260 ft/sec.
Overall, I want to relate hertz to a speed in mph to mentally understand how fast a hertz is?View Full Posting Details