A truck travels beneath an airplane that is moving 150 km/h at an angle of 34◦ to the ground. How fast must the truck travel to stay beneath the airplane?

Answer in units of km/h.

154 cos34°

154 cos(34) = 127.67178....

To solve this problem, we need to find the horizontal component of the airplane's velocity and match it with the truck's velocity.

Given:
Airplane's velocity = 150 km/h
Angle of airplane to the ground = 34°

To find the horizontal component of the airplane's velocity, we can use the formula:
horizontal velocity = total velocity * cosine(angle)

horizontal velocity = 150 km/h * cosine(34°)
horizontal velocity = 150 km/h * 0.829 (rounded to 3 decimal places)
horizontal velocity = 124.35 km/h (rounded to 2 decimal places)

Therefore, the truck must travel at a speed of 124.35 km/h to stay beneath the airplane.

To find out how fast the truck must travel to stay beneath the airplane, we need to consider the horizontal and vertical components of motion separately.

Let's start with the horizontal component. Since the truck needs to stay beneath the airplane, the horizontal component of the truck's velocity must be equal to the horizontal component of the airplane's velocity. The horizontal component of the airplane's velocity can be found using the formula:

Horizontal component of velocity = Speed of the airplane × cos(angle)

Given that the airplane is moving at 150 km/h at an angle of 34° to the ground, we can calculate the horizontal component of the airplane's velocity as follows:

Horizontal component of velocity = 150 km/h × cos(34°)

Now, let's move on to the vertical component. We can ignore the vertical component because it does not affect the truck's ability to stay beneath the airplane.

Therefore, to find the required velocity of the truck, we only need to consider the horizontal component of the airplane's velocity.

Horizontal component of velocity = 150 km/h × cos(34°)
≈ 124.84 km/h

Hence, the truck must travel at a speed of approximately 124.84 km/h to stay beneath the airplane.