A rocket is launched into the air verically is tracked by a radar station on the ground 3 km from the launch site. What is the veritcal speed of the rocket at the instant when the distance from the radar station is 5 km and this distance is increasing at a rate of 5 000km/hr ???
The height of the rocket at that time is sqrt (5^2 - 3^2) = 4 km
Let x = distance to the rocket and h = height.
x^2 = h^2 + 9
2x dx/dt = 2h dh/dt
10 * 5000 = 8 * dh/dt
dh/dt = vertical speed = 50,000/8 = 6250 km/hr
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