Final answer:
To solve for the speed of the other car, you use the Pythagorean theorem with the police speed and radar measurement to find the other car's speed. The calculation gives us approximately 31.24 mph; thus, the speed of the other car is closest to 30 mph, which is option A.
Step-by-step explanation:
The student is asking to calculate the speed of another car using a given radar gun measurement. The police officer is driving north towards an intersection, and the other car is driving east away from the intersection. The radar gun is indicating an increase in distance at a rate of 25 mph.
To solve this, we recognize this as a right-angle triangle problem with the police car moving north and the other car moving east. We can use the Pythagorean theorem where the hypotenuse is the radar reading and the legs of the triangle are the speeds of the police car and the other car, respectively. Since we know the police car's speed (40 mph) and the radar's measurement of the increasing distance (25 mph), we can find the speed of the other car.
The relationship is described by the equation:
radar2 = police2 + other_car2
252 = 402 + other_car2
625 = 1600 + other_car2
other_car2 = 625 - 1600
other_car2 = -975, which is not possible, indicating an error in the calculation. The correct calculation should be:
other_car2 = 1600 - 625
other_car2 = 975
other_car = √975 ≈ 31.24 mph
So the closest answer from the choices given is A) 30 mph.