A police helicopter is flying at 150 mph at a constant altitude of 0.5 mile above a straight road. The pilot uses radar to determine that an oncoming car is at a distance of exactly 1 mile from the helicopter, and that this distance is decreasing at 190 mph. Find the speed of the car. (a) Draw a picture of the situation for any time t. (b) What quantities are given in the problem

a) (see attached picture)

b) d, h, velocity of helicopter, dd/dt

in the direction oposite to the movement of the helicopter.

Step-by-step explanation:

In order to solve this problem we must start by drawing a diagram that will represent the situation (see attached picture). As you may see, there is a right triangle being formed by the helicopter, the car and the graound. We can use this to build the equation we are going to use to model the problem.

we can use this equation to find the value of x at that very time, so we can do that by solving the equation for x, so we get:

and substitute the given values:

which yields:

x=0.866mi

we know that the height of the helicopter is going to be constant, so we rewrite the equation as:

Next, we can go ahead and differentiate the equation so we get:

which can be simplified to:

we can next solve the equation for dx/dt so we get:

so we can now substitue te provided values so we get:

so we get:

the negative sign means that the x-value is decreasing.

now, this problem deals with relative velocities, so we get that:

Velocity of car about the helicopter = Velocity of the car - Velocity of the helicopter. Or:

so we can solve this for the actual velocity of the car, so we get:

so we get:

which yields:

So it has a velocity of 69.4mph in a direction oposite to the helicopter's movement.

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