Answer :
Answer:
At 28.93 km/min is the distance from the plane to the radar station increasing 5 minutes later
Step-by-step explanation:
We are given A plane flying with a constant speed of 29 km/min passes over a ground radar station at an altitude of 15 km
Refer the attached figure
[tex]\angle A =45+90=135^{\circ}\\\frac{dy}{dt}=29[/tex]
x=15
[tex]y=5 \times 29=145[/tex]
We will use cosine law
[tex]z^2=x^2+y^2-2xycos A\\z^2=15^2+y^2-2(15)ycos 135\\z^2=225+y^2-30ycos135 ----1\\z^2=225+(145)^2-30(145)cos135[/tex]
z=155.96 km
Differentiating 1 w.r.t t
[tex]2z\frac{dz}{dt}=2y\frac{dy}{dt}-30cos 135 \frac{dy}{dt}[/tex]
[tex]2(155.96)\frac{dz}{dt}=2(145)(29)-30cos 135 (29)[/tex]
[tex]\frac{dz}{dt}=\frac{2(145)(29)-30cos 135 (29)}{2(155.96)}[/tex]
[tex]\frac{dz}{dt}=28.93[/tex]
Hence At 28.93 km/min is the distance from the plane to the radar station increasing 5 minutes later