A plane flying with a constant speed of 14 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 is the distance from the plane to the radar station increasing 3 minutes later?
Accepted Solution
A:
Answer:the rate from the plane to the radar station increasing 3 minutes later is 19.81 km/minStep-by-step explanation:A plane flying with a constant speed of 14 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 is the distance from the plane to the radar station increasing 3 minutes later?speed (Δs₁)= change in distance(Δd₁) /(Δt₁)change in timemathematically, [tex]\frac{Δd₁}{Δt₁}[/tex] = Δs₁= 14 km/min = [tex]\frac{Δd}{Δt}[/tex]and will are to find the speed after passes the radar=Δs₂ km/min = [tex]\frac{Δd₂}{Δt₂}[/tex]to find d₁ and d₂ with respect to angle 45 degree at 4kmsin 45 = opp/hyp = 4/d₁d₁ = 4/sin45 = 5.66kmtan 45 == opp/adj = 4/d₂d₂ =4/tan45 = 4kmfor three minute increment, =3 x d₁ x Δs₁ = 3 x d₂ Δs₂ = 3x5.66x14 = 3x 4 xΔs₂= 237.72 = 12Δs₂=Δs₂ = 19.81km/min