Question

A plane flying with a constant speed of 150 km/h passes over a ground radar station at an altitude of 3 km and climbs at an angle of 30°. At what rate is the distance from the plane to the radar station increasing a minute later? (Round your answer to the nearest whole number.)

Answer 1

Answer:

Explanation:

Total angle at point A = 30°+90° = 120°

Speed = 150 km/hr = 2.5 km/min

therefore Distance travelled by plane in 1 minute is 2.5 km.

c =2.5 km

by law of cosine

a^2 = b^2+c^2 -2bc cosA

a^2 = 1^2+c^2 -2*1*c cos120°

a^2 = 1+c^2 + c ................................................1

a^2 = 1^2+c^2 -2*1*2.5 cos120°

a^2 = 2.5+1+ 2.5^2

a =3.12

now differentiate the equation 1 w.r.t t to obtained $\frac{da}{dt}$ value

$a^2 = 1+c^2 + c$

$2a\frac{da}{dt} = 0+2c\frac{dc}{dt} =\frac{dc}{dt}$

$\frac{da}{dt} =\frac{2c+1)\frac{dc}{dt}}{2a}$

            $=\frac{2*2.5+1)*2.5}{2*3.12}$

$\frac{da}{dt} =2.40 km/min = 144.23 km/hr$