Caculas
posted by matthew .
(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.

x^2 + h^2 = D^2
solve for x when D = 10 and h = 6
x = 8 (3,4,5 triangle)
2 x dx/dt + 2 h dh/dt = 2 D dD/dt
but dh/dt = 0
so
2 (8)v + 0 = 2 (10) 300
v = 3000/8
Respond to this Question
Similar Questions

MATH
A plane flying with a constant speed of 24 km/min passes over a ground radar station at an altitude of 4 km and climbs at an angle of 45 degrees. At what rate, in km/min, is the distance from the plane to the radar station increasing … 
Calc
A plane that is flying horizontally at an altitude of 6 kilometers and a speed of 680 kilometers per hour passes directly over a radar station. How fast is the distance between the plane and the radar station increasing when the distance … 
Calc
An airplane is flying at a speed of 350 mi/h at an altitude of one mile and passes directly over a radar station at time t=0. a) Express the horizontal distance d (in miles) that the plane has flown as a function of t. I really don't … 
Calculus
An airplane is flying at a speed of 350 mi/h at an altitude of one mile and passes directly over a radar station at time t=0. a) Express the horizontal distance d (in miles) that the plane has flown as a function of t. b) Express the … 
PRECALCULUS
An airplane is flying at a speed of 250 mph at an altitude of 4 miles. The plane passes directly above a radar station at time t=0. Find the distance s between the plane and the radar station after 5 minutes. 
Airplane & Radar
(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 … 
calculus
A plane that is flying horizontally at an altitude of 6 kilometers and a speed of 570 kilometers per hour passes directly over a radar station. How fast is the distance between the plane and the radar station increasing when the distance … 
CALCULUS
A plane, flying horizontally at an altitude of 1 km and a speed of 500 km/hr, passes directly over a radar station. find the rate in km/hr at which the distance from the plane to the station is changing when it is 2 km away from the … 
PreCalc
An airplane is flying at a speed of 250 mph at an altitude of 4 miles. The plane passes directly above a radar station at time t = 0. What is the distance s between the plane and the radar station after four minutes? 
Calc
An airplane is flying at a speed of 350 mi/h at an altitude of one mile and passes directly over a radar station at time t=0. a) Express the horizontal distance d (in miles) that the plane has flown as a function of t. I really don't …