Question

Two cars are driving away from an intersection in perpendicular directions. The first car's velocity is 777 meters per second and the second car's velocity is 333 meters per second. At a certain instant, the first car is 555 meters from the intersection and the second car is 121212 meters from the intersection. What is the rate of change of the distance between the cars at that instant (in meters per second)?

Answer 1

Answer:

The rate of change of the distance between the cars at that instant is 5.46 meters per second

Step-by-step explanation:

Speed of first car = 7 m/s

Speed of second car = 3 m/s

At instant, distance of first car from intersection = 5 meters

distance of second car from intersection = 12 meters

Therefore, we have

Distance between both cars at intant = √(12² + 5²) = 13 m

Rate of cahnge of distance is given by;

2ddd/dt = d(x² + y²)/dt = 2xdx/dt + 2ydy/dt

= 26dd/dt = 2×5×7 + 2×12×3 = 142

dd/dt = 142/26 = 5.46 m/s.

That is the rate of change of the distance between the cars at that instant = 5.46 meters per second.