Question

A plane flying with a constant speed of 29 km/min passes over a ground radar station at an altitude of 15 km and climbs at an angle of 45 degrees. At what rate is the distance from the plane to the radar station increasing 5 minutes later

Answer 1

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

`\angle A =45+90=135^(\circ)\\(dy)/(dt)=29`

x=15

`y=5 * 29=145`

We will use cosine law

`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`

z=155.96 km

Differentiating 1 w.r.t t

`2z(dz)/(dt)=2y(dy)/(dt)-30cos 135 (dy)/(dt)`

`2(155.96)(dz)/(dt)=2(145)(29)-30cos 135 (29)`

`(dz)/(dt)=(2(145)(29)-30cos 135 (29))/(2(155.96))`

`(dz)/(dt)=28.93`

Hence At 28.93 km/min is the distance from the plane to the radar station increasing 5 minutes later