Question

A sports car at point A drives down a straight stretch of road CD. A police car at point B uses radar to measure the speed of the car, and obtains a reading of 51 km/h. For the position of the car given below, determine the speed of the car. Note that the 51 km/h speed measured by the radar gun is the rate of change of the distance between the car and the radar gun. The car is 30% of the distance from point C to point D. B(75,600,40)m C(-150,-50,30)m D(200,400,-10)m Actual speed of the car: km/h

Answer 1

To determine the speed of the car, calculate the distance between the car and point C, then calculate the total distance between points C and D, and finally use the ratios to find the speed of the car.

Step-by-step explanation:

The speed of the car can be determined by finding the rate of change of the distance between point C and the car. Let's calculate the distance between the car and point C:

Distance = √[(200 - (-150))^2 + (400 - (-50))^2 + ((-10) - 30)^2]

Distance = √[350^2 + 450^2 + 40^2]

Distance = √[122500 + 202500 + 1600]

Distance = √326600

Since the car is 30% of the distance from C to D, we can calculate the total distance between C and D:

Total Distance = Distance from C to D = √[(200 - (-150))^2 + (400 - (-50))^2 + ((-10) - 30)^2]

Total Distance = √326600

Finally, we can find the speed of the car by multiplying the measured speed of 51 km/h by the ratio of the distance of the car from C to D to the total distance between C and D:

Car Speed = 51 km/h * (30% of Distance from C to D) / (Total Distance)

Learn more about speed of car