Respuesta :
Answer:
102 km/h
Explanation:
x = distance of car A at any time from the intersection
x₀ = distance of car A at some time = 0.4 km
[tex]v_{A}[/tex] = Speed of car A = 75 km/h
y = distance of car B at any time from the intersection
y₀ = distance of car B at some time = 0.3 km
[tex]v_{B}[/tex] = Speed of car B = 70 km/h
d = distance between the two cars at any time
d₀ = distance between the two cars at some time
v = rate of change of distance between the cars
Using Pythagorean theorem
d²₀ = x₀² + y₀²
d²₀ = 0.4² + 0.3²
d₀ = 0.5 m
Distance between the two cars at any time is given using Pythagorean theorem as
d² = x² + y²
Taking derivative both side relative to "t"
[tex]2d \left ( \frac{dd}{dt} \right ) = 2x ( \frac{dx}{dt} \right ) + 2y ( \frac{dy}{dt} \right )[/tex]
[tex]d_{o} v = x_{o} ( \frac{dx}{dt} \right ) + y_{o} ( \frac{dy}{dt} \right )[/tex]
(0.5) v = (0.4) [tex]v_{A}[/tex] + (0.3) [tex]v_{B}[/tex]
(0.5) v = (0.4) (75) + (0.3) (70)
v = 102 km/h
