A woman in a car on a level road sees an airplane traveling in the same direction that is climbing at an angle of 30 degrees above the horizontal. By driving 110 km/h she is able to stay directly below the airplane. What is the airplane's velocity?

110÷cos30=127km/h

v cos 30 = 110

127 Vcos30° = 110

To find the airplane's velocity, we need to break down its motion into horizontal and vertical components. Let's assume the airplane's velocity is v and the horizontal component of its velocity is vx, while the vertical component is vy.

Now, since the car is directly below the airplane, its horizontal velocity must be equal to the horizontal component of the airplane's velocity. Since the car is driving at 110 km/h, its horizontal velocity is also 110 km/h.

To find the vertical component of the airplane's velocity (vy), we can use the trigonometric relationship between the angle of climb (30 degrees) and the vertical component of velocity.

sin(30°) = vy / v

Rearranging the equation, we get:

vy = v * sin(30°)

Now, we can also relate the car's velocity (110 km/h) to the vertical and horizontal components of airplane velocity:

vx = 110 km/h
vy = v * sin(30°)

The horizontal and vertical components of the velocity combine to give the overall velocity. We can use the Pythagorean theorem to find v:

v = √(vx^2 + vy^2)

Plugging in the values, we get:

v = √((110 km/h)^2 + (v * sin(30°))^2)

Simplifying the equation, we have:

v = √(12100 + (v^2 * 0.25))

Squaring both sides of the equation, we get:

v^2 = 12100 + (v^2 * 0.25)

Multiplying out, we have:

v^2 = 12100 + 0.25v^2

Simplifying further, we get:

0.75v^2 = 12100

Dividing both sides by 0.75, we have:

v^2 = 16133.33

Taking the square root of both sides, we get:

v ≈ 127.02 km/h

Therefore, the airplane's velocity is approximately 127.02 km/h.