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.

Question

Chung

Mathematics

13 March, 22:42

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.

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Answers (1)

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Paul Duncan · Answer 1

Answer: 62 mph

Step-by-step 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