a police helicopter is flying at 200 km/hr at a constant altitude of 1 km above a straight road. The pilot uses radar to determine that an oncoming car is at a distance of exactly 2 km from the helicopter, and that this distance is decreasing at 250 km/hr. Find the speed of the car.

133.33

To find the speed of the car, we can use the concept of relative velocity.

Let's consider the motion of the car from the helicopter's reference frame. Since the distance between the car and the helicopter is decreasing, the velocity of the car relative to the helicopter is the difference between their velocities.

The velocity of the helicopter is given as 200 km/hr, and we need to convert the car's velocity from km/hr to m/s. Hence, we first convert the car's velocity from km/hr to m/s:

Velocity of car = 250 km/hr = (250 * 1000 m) / (60 * 60 s) = 69.4 m/s (approximately)

Next, we subtract the helicopter's velocity from the car's velocity to find the relative velocity of the car with respect to the helicopter:

Relative velocity = Velocity of car - Velocity of helicopter
= 69.4 m/s - 200 km/hr
= 69.4 m/s - (200 * 1000 m) / (60 * 60 s)
= 69.4 m/s - 55.56 m/s
= 13.84 m/s

Therefore, the speed of the car in the reference frame of the road is 13.84 m/s.