Marta is standing 4 ft behind a fence 6 ft 6 in. tall. When she looks over the fence, she can just see the top edge of a buildin
g. She knows that the building is 32 ft 6 in. behind the fence. Her eyes are 5 ft from the ground. How tall is the building? Give your answer to the nearest half foot.
1 answer:
Answer: 93ft
Explanation: Martha's eyesight make an angle with the fence, this is solved as a triangle problem.
We first convert all the dimensions to inches using the fact that 12 inches make 1 ft.
To solve for the angle
Tan § = 18/48 = 0.375
§ = tan^-1 of 0.375 = 20.55°
This same angle elevates to the edge of the building
Tan 20.55 = 399/x
x = 399/tan 20.55
x = 1040 inches
Height of building = x + height of fence
Height of building = 1040 + 78 = 1118 inches
Converting back to ft it becomes
1118/12 = 93 ft 2 inches
Approximately 93ft
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Answer:
The torque on the pulley, when the system is motionless is approximately 9.81 N·m
Explanation:
The given parameters are;
The mass of the object = 2 kg
The friction between the rope and the pulley = 0
The mass of the rope, = 0.5 kg
The mass of the pulley, = 0.01 kg
The radius of the pulley, r = 0.25 m
The torque on the pulley, τ = I·α = F × D
The torque on the pulley, when the system is motionless, τ = F × D
Where;
F = The force acting on the pulley rope = The weight of the mass ≈ 2 kg × 9.81 m/s² = 19.62 N
D = The diameter of the pulley = 2×r = 2 × 0.25 m = 0.5 m
Therefore;
τ = 19.62 N × 0.5 m = 9.81 N·m
The torque on the pulley, when the system is motionless, τ ≈ 9.81 N·m.