A small blimp is used for advertising purposes at a football game. It has a mass of 93.0 kg and is attached by a towrope to a truck on the ground. The towrope makes an angle of 53.3° downward from the horizontal, and the blimp hovers at a constant height of 20.7 m above the ground. The truck moves on a straight line for 783.4 m on the level surface of the stadium parking lot at a constant velocity of 9.0 m/s. If the drag coefficient (K in

F = Kv2)
is 0.5 kg/m, how much work is done by the truck in pulling the blimp (assuming there is no wind)?

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To find the work done by the truck in pulling the blimp, we need to calculate the net force acting on the blimp and then multiply it by the displacement of the truck.

Step 1: Calculate the gravitational force on the blimp.
The gravitational force can be calculated using the formula:
F_gravity = mass of the blimp * acceleration due to gravity
F_gravity = 93.0 kg * 9.8 m/s^2
F_gravity = 911.4 N

Step 2: Calculate the vertical component of the tension force in the towrope.
The vertical component of the tension force can be calculated using the formula:
F_vertical = F_gravity

Step 3: Calculate the horizontal component of the tension force in the towrope.
The horizontal component of the tension force can be calculated using the formula:
F_horizontal = F_horizontal = F_tension * sin(angle)
F_horizontal = F_vertical * sin(53.3°)
F_horizontal = 911.4 N * sin(53.3°)
F_horizontal = 711.1 N

Step 4: Calculate the drag force.
The drag force can be calculated using the formula:
F_drag = drag coefficient * velocity^2
F_drag = 0.5 kg/m * (9.0 m/s)^2
F_drag = 36.0 N

Step 5: Determine the net horizontal force.
The net horizontal force can be calculated by subtracting the drag force from the horizontal component of the tension force:
F_net = F_horizontal - F_drag
F_net = 711.1 N - 36.0 N
F_net = 675.1 N

Step 6: Calculate the work done by the truck.
Work = force * displacement
Work = F_net * displacement
Work = 675.1 N * 783.4 m
Work = 529,238.34 Joules

Therefore, the truck does approximately 529,238.34 Joules of work in pulling the blimp.

To find the amount of work done by the truck in pulling the blimp, we need to calculate the net force acting on the blimp in the direction of motion and then multiply it by the distance traveled.

Step 1: Find the horizontal component of the tension in the towrope.
The tension in the towrope can be split into horizontal and vertical components. The horizontal component is responsible for moving the blimp forward.

Tension_horizontal = Tension * cos(θ)
where θ is the angle made by the towrope with the horizontal.

In this case, the angle is given as 53.3° downward from the horizontal, so the angle with the horizontal is 90° - 53.3° = 36.7°.

Tension_horizontal = Tension * cos(36.7°)

Step 2: Find the drag force acting on the blimp.
The drag force is given by the equation F = Kv², where F is the drag force, K is the drag coefficient, and v is the velocity of the blimp relative to the air.

Here, the blimp is assumed to have no wind, so the velocity of the blimp relative to the air is the same as the velocity of the truck, which is 9.0 m/s.

Drag_force = K * v²

Step 3: Find the net force acting on the blimp.
The net force is the vector sum of the horizontal tension force and the drag force. Since the blimp hovers at a constant height, the vertical forces cancel out.

Net_force = Tension_horizontal - Drag_force

Step 4: Calculate the work done.
The work done is given by the equation W = force * distance.

Work_done = Net_force * distance

Substitute the given values into the above equations and solve to find the work done by the truck.