(Airplane & Radar) An airplane is flying (horizontally) at the height of 6 km on a flight path that will take it
directly over a radar tracking station (on ground). If the distance D between the plane and the radar is
decreasing at a rate of 300 km/hr, find the speed of the plane when D remains 10 km.
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To find the speed of the plane when the distance D remains 10 km, we need to consider the relationship between the distance D and the rate at which it is decreasing.
Let's assume that the speed of the plane is V km/hr.
We know that the rate of change of distance D with respect to time is given as -300 km/hr (negative because the distance is decreasing).
Using the chain rule of differentiation, we can relate the rate of change of distance D with respect to time (dD/dt) to the speed of the plane (V) and the rate of change of height with respect to time (dh/dt).
Since the plane is flying horizontally, the rate of change of height with respect to time (dh/dt) is zero.
Therefore, we have the following relationship:
dD/dt = - (dh/dt)
Substituting the given rate of change of distance (dD/dt = -300 km/hr) and the rate of change of height (dh/dt = 0), we get:
-300 = 0
This equation implies that the speed of the plane (V) is also 0 km/hr.
Therefore, the speed of the plane when the distance D remains 10 km is 0 km/hr.