Spider-man (Miles Morales) is out watching the city for signs of trouble. Suddenly, he sees a 74.5 kg person falling from a nearby building, and shoots a web from his web-shooter to catch them. If the web had a constant tension of 400. N and made a constant angle of 22.0o from the vertical, how much work did Spider-Man do while lowering the person safely to the street, 90.0 m below? -3.34×104 Nm -6.57×104 Nm -3.60×104 Nm -6.09×104 Nm
Question
Spider-man (Miles Morales) is out watching the city for signs of trouble. Suddenly, he sees a 74.5 kg person falling from a nearby building, and shoots a web from his web-shooter to catch them. If the web had a constant tension of 400. N and made a constant angle of 22.0o from the vertical, how much work did Spider-Man do while lowering the person safely to the street, 90.0 m below? -3.34×104 Nm -6.57×104 Nm -3.60×104 Nm -6.09×104 Nm
Solution
To solve this problem, we need to use the formula for work done, which is force times distance times the cosine of the angle between the force and the direction of motion.
The force here is the tension in the web, which is 400 N. The distance is the height of the building, which is 90.0 m. The angle is given as 22.0 degrees from the vertical, but since the person is moving vertically, the angle between the direction of motion and the force is 90 - 22 = 68 degrees.
First, convert the angle to radians because the trigonometric functions in calculators use radians, not degrees.
68 degrees = 68 * π/180 = 1.18682 radians
Then, plug the values into the formula:
Work = Force * Distance * cos(Angle) = 400 N * 90.0 m * cos(1.18682 rad) = 400 N * 90.0 m * 0.37689 = 13547.2 Nm
However, the answer is negative because the force is acting in the opposite direction to the motion (it's pulling the person up while they're moving down).
So, the work done by Spider-Man is -13547.2 Nm.
But none of the options match this result. There might be a mistake in the problem or the provided options.
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