Answer:
30 m/s
Step-by-step explanation:
Let's say the distance from the first car to the intersection is x, and the distance from the second car to the intersection is y.
The distance between the cars can be found with Pythagorean theorem:
d² = x² + y²
Taking derivative with respect to time:
2d dd/dt = 2x dx/dt + 2y dy/dt
d dd/dt = x dx/dt + y dy/dt
We know that x = 200, dx/dt = -25, y = 150, and dy/dt = -50/3.
To find dd/dt, we still need to find d.
d² = x² + y²
d² = (200)² + (150)²
d = 250
Plugging everything in:
250 dd/dt = (200) (-25) + (150) (-50/3)
dd/dt = -30
The cars are approaching each other at a rate of 30 m/s at that instant.
