An airplane is flying 320 km/h N25degreesW and a unexpected wind is affecting it that has a velocity of 35 km/h S20degreesW Find the resultant velocity.
An airplane is flying 320 km/h N25degreesW and a unexpected wind is affecting it that has a velocity of 35 km/h S20degreesW. Find the resultant velocity.
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We can separate the two velocities into right angled components and add them separately and then find the resultant velocity. We can find the components in North and West directions. Therefore let y be North direction and x be west direction.
`u_y = 320 xx cos(25) = 290` km/h
`u_x = 320 xx sin(25) = 135.28` km/h
`v_y = -35 xx cos(20) = -32.89` km/h
v_x = 35 xx sin(20) = 11.97
Therefore resultant components are,
`w_y = u_y+v_y`
`w_y = (290-32.89)` km/h
`w_y = 257.11` km/h
`w_x = u_x+v_x`
`w_x = (135.28+11.97)` km/h
`w_x = 147.25` km/h
Therefore the resultant velocity is,
`w = sqrt(257.11^2+147.25^2)`
`w = 296.29` km/h
The angle or direction with North.
`tan(alpha) = 147.25/257.11 = 0.5727`
`alpha = tan^(-1)(0.5727) = 29.78` degrees.
Therefore the resultant velocity is 296.29 km/h N29.78 degrees W.
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