physics (speed of plane by radar)

The radar stations A and B, separated by the distance a = 500 m, track the plane C by recording the angles α and β at 1-second intervals,
If three successive readings are shown in the table,calculate the speed v of the plane and the climb angle y at t = 10 seconds as accurate as you can.

The coordinates of the plane can be shown to be:

x = a ((tan β)/(tan β – tan α)

y = a ((tan α tan β)/(tan β – tan α) (height to plane)


t/sec 9 10 11

α (degrees) 54.80 54.06 53.34

β (degrees) 65.59 64.59 63.62

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