Question

A highway patrol plane flies 1 mile above a flat, straight road at a steady ground speed of 120 miles per hour. The pilot sees an oncoming car and, with radar, determines that the line-of-sight distance from the plane to the car is 1.5 miles, decreasing at the rate of 136 miles per hour. Find the car’s speed along the highway.

Answer 1

Answer: 62 mph

Explanation:

Given that patrol plane is 1 mile above a flat, straight road

Let h = 1 mile

The horizontal distance x will be achieved by using pythagorean theorem

1.5^2 = h^2 + x^2

x^2 = 2.25 - 1

x = 1.12 miles

Since it is decreasing at the rate of 136 miles per hour, the car will be moving close at

1.12 × speed = 1.5 × 136

Speed = 204/1.12 = 182 mph

Since the plane moves at 120 mph

The the car’s speed along the highway will be

Speed = 120 - 182 = 62 mph