Question

Plane A and B ate both flying eastward with constant velocity in the same horizontal plane at angles 30 degrees and 60 degrees with respect to the horizontal respectively. The speed of A is 100 square root of 3 miles per second. Initially, the pilot of plane A sees plane B directly ahead at the same altitude at a horizontal distance of 500 meters. Assuming the two planes will not change directions and altitude, kn how many seconds will plane A crash with plane B?

Answer 1

they must be flying in the same vertical plane, if they are traveling with an angle relative to the horizontal ...

Also, I suspect A's speed is 100√3 m/s, not mi/s.

Using the law of cosines,

500^2 + (100√3 t)^2 - 2(500)(100√3 t)(√3/2) = (100√3 t)^2

They will crash in 5/3 seconds.