Answer:
Option C - 52 mph
Step-by-step explanation:
I've attached an image to depict the diagram of movement of both cars.
dy/dt = 50 mph
dx/dt = 20 mph
From the attached image, using pythagoras theorem, we have;
x² + y² = s²
Differentiating with respect to to using implicit differentiation with power rule, we have;
2x(dx/dt) + 2y(dy/dt) = 2s(ds/dt) - - (eq1)
Now, let's find s by pythagoras theorem.
s² = 0.375² + 0.5²
s² = 0.390625
s = √0.390625
s = 0.625
Plugging in all the relevant values into eq 1,we have;
2×0.375(20) + 2×0.5(50) = 2×0.625(ds/dt)
15 + 50 = 1.25(ds/dt)
65 = 1.25(ds/dt)
ds/dt = 65/1.25
ds/dt = 52 mph
