Question

Two planes take off at the same time from an airport. The first plane is flying at 240 miles per hour on a bearing of S 45.0° E. The second plane is flying in the direction S 45.0°W at 275 miles per hour. If there are no wind currents blowing, how far apart are they after 5 hours? What is the bearing of the second plane from the first after 5 hours?

Answer 1

The distance between the two planes after 5 hours is approximately 1200 miles, and the bearing of the second plane from the first is S 45.0° E.

Step-by-step explanation:

To find the distance between the two planes after 5 hours, we can use the formula:

Distance = Speed × Time

For the first plane, the distance it travels after 5 hours is:

240 miles/hour × 5 hours = 1200 miles

For the second plane, the distance it travels after 5 hours is:

275 miles/hour × 5 hours = 1375 miles

To find the bearing of the second plane from the first after 5 hours, we can use trigonometry. Since both planes are flying at a 45.0° angle, the bearing can be calculated as:

tan(45.0°) = Opposite/Adjacent

tan(45.0°) = Distance of second plane/Distance of first plane

Solving for the distance of the second plane, we get:

Distance of second plane = tan(45.0°) × Distance of first plane

Using the distance values we calculated earlier:

Distance of second plane = tan(45.0°) × 1200 miles

Distance of second plane ≈ 1200 miles

Therefore, the two planes are approximately 1200 miles apart after 5 hours, and the bearing of the second plane from the first is also approximately S 45.0° E.