Respuesta :
Answer:
[tex]\frac{ds}{dt} = 39.586 km/h[/tex]
Step-by-step explanation:
let distance between farmhouse and road is 2 km
From diagram given
p is the distance between road and past the intersection of highway
By using Pythagoras theorem
[tex]s^2 = 2^2 +p^2[/tex]
differentiate wrt t
we get
[tex]\frac{d}{dt} s^2 = \frac{d}{dt} (4 + p^2)[/tex]
[tex]2s \frac{ds}{dt} =2p \frac{dp}{dt} [/tex]
[tex]\frac{ds}{dt} = \frac{p}{s}\frac{dp}{dt}[/tex]
[tex]\frac{ds}{dt} = \frac{p}{\sqrt{p^2 +4}} \frac{dp}{dt}[/tex]
putting p = 3.7 km
[tex]\frac{ds}{dt} = \frac{3.7}{\sqrt{3.7^2 +4}} 45[/tex]
[tex]\frac{ds}{dt} = 39.586 km/h[/tex]
