A fire helicopter carries a 565 kg bucket

at the end of a 16.7 m long cable. When
the helicopter is returning from a fire at a
constant speed of 22.5 m/s, the cable makes
an angle of 20.5
◦ with respect to the vertical.
Find the horizontal force exerted by air
resistance on the bucket. The acceleration
due to gravity is 9.8 m/s
2
.
Answer in units of N

To find the horizontal force exerted by air resistance on the bucket, we need to analyze the forces acting on the bucket.

1. First, let's find the tension in the cable. The tension in the cable can be broken down into two components: vertical and horizontal.

The vertical component of tension is responsible for supporting the weight of the bucket and can be calculated using the following equation:
T_vertical = m * g,
where m is the mass of the bucket (565 kg) and g is the acceleration due to gravity (9.8 m/s^2).

T_vertical = 565 kg * 9.8 m/s^2.

The horizontal component of the tension is what we want to find, so let's call it T_horizontal.

2. Next, let's calculate the angle between the cable and the vertical line. The angle is given as 20.5 degrees.

3. Now, we can use trigonometry to find the horizontal component of the tension.
T_horizontal = T * sin(angle),
where T is the tension in the cable.

T_horizontal = T * sin(20.5 degrees).

4. Finally, we can substitute T_vertical into the equation for T_horizontal to get the value of the horizontal force exerted by air resistance on the bucket.

T_horizontal = (565 kg * 9.8 m/s^2) * sin(20.5 degrees).

Calculating this expression will give us the horizontal force in units of Newtons (N).