Answer:
the rate from the plane to the radar station increasing 3 minutes later is 19.81 km/min
Step-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 time
mathematically,
[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 4km
sin 45 = opp/hyp = 4/d₁
d₁ = 4/sin45 = 5.66km
tan 45 == opp/adj = 4/d₂
d₂ =4/tan45 = 4km
for three minute increment,
=3 x d₁ x Δs₁ = 3 x d₂ Δs₂
= 3x5.66x14 = 3x 4 xΔs₂
= 237.72 = 12Δs₂
=Δs₂ = 19.81km/min
