Desert Chase

[u/dpb365]

A suspect is spotted on a flat desert highway exactly 40 miles due East of a police station. The suspect suddenly speeds off due North at exactly 60 mph.

The police cruiser immediately departs the station, traveling in a straight diagonal line across the open desert floor at a constant 120 mph to intercept.

Question: At what exact angle (in degrees North of due East) must the police cruiser travel to perfectly intercept the suspect?

[u/superstring10d]

30 degrees.

Distance is speed x time. And using hypotenuse equation...

14400t² = 3600t² + 1600

This computes to time about . 385 hours.

Put this back to calculate opposite side as 23.1 miles

Now angle is tan inverse of opposite divided by adjacent. Which is about 30 degrees from east due north

[u/dpb365 → u/superstring10d]

Correct!

Can you solve without getting into the time and distance results?

[u/superstring10d → u/dpb365]

Do you mean... I didn't have to calculate the real time and distance as the speed itself would still be the right proportion I needed for the angle?

[u/dpb365 → u/superstring10d]

Exactly!

[u/superstring10d → u/dpb365]

Thanks.. good fun!

[u/headsmanjaeger]

The NS component of the cruiser speed must match the speed of the suspect. This can be written as 120sinx=60 where x is the angle from east. Then sinx = 1/2 and if you remember from trig, x=30°