Question

A truck travels beneath an airplane that is moving 120 km/h at an angle of 24◦ to the ground.

How fast must the truck travel to stay beneath the airplane?

Answer 1

Vt = 120cos24 = 18.27km/h.

Answer 2

hey im typing that in my caculator and its not getting 18.27. what am I doing wrong?

Answer 3

Type 120arccos(24)

Answer 4

109.625

Answer 5

[AI-generated answer — Explain Bot]

To determine how fast the truck must travel to stay beneath the airplane, we need to find the horizontal speed component of the airplane.

Given:
Airplane's speed = 120 km/h
Angle of the airplane with respect to the ground = 24 degrees

To find the horizontal speed of the airplane, we can use trigonometry. The horizontal speed component of the airplane is given by:

horizontal speed = airplane's speed * cosine(angle)

So, the horizontal speed of the airplane is:

horizontal speed = 120 km/h * cos(24 degrees)

Using a calculator, we can evaluate the cosine of 24 degrees:

cos(24 degrees) ≈ 0.9135

Now, we can calculate the horizontal speed of the airplane:

horizontal speed = 120 km/h * 0.9135 ≈ 109.62 km/h

Therefore, the truck must travel at a speed of approximately 109.62 km/h to stay beneath the airplane.