Determining the Value of v for Plane Collision

When do Plane 1 and Plane 2 collide?

Given the distance between the two cities, the speeds of the planes, and the departure times, for which value of v will Plane 1 and Plane 2 collide?

Answer: v = 142.85 mph

Explanation: The value of v at which Plane 1 and Plane 2 collide is 142.85 mph. This value is determined by calculating the positions of both planes at a specific time. Plane 1 arrives at City B at 11 am after 4 hours of travel. To collide with Plane 1, Plane 2 must reach City B before 11 am.

To determine the value of v at which Plane 1 and Plane 2 collide, we need to calculate the positions of both planes at a certain time. Since Plane 1 travels at a constant speed of 250 mph towards City B, it will reach City B after 1000 miles / 250 mph = 4 hours. Therefore, Plane 1 will be at City B at 11 am (7 am + 4 hours).

Now, to find the position of Plane 2 at 11 am, we need to calculate the time it takes for Plane 2 to reach City B. Plane 2 leaves City C at 7:30 am and flies towards City A, located 400 miles North of City A. It will take Plane 2 3.33 hours (1000 miles / 300 mph) to reach City A. Therefore, Plane 2 will be at City A at 10:48 am (7:30 am + 3.33 hours).

Since the planes collide at the same time, Plane 2 must reach City B in less time than Plane 1. Therefore, the value of v should exceed 250 mph to allow Plane 2 to reach City B before Plane 1.