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Part 1
A magnitude of 600 pounds of force is required to hold a boat and its trailer in place on a ramp whose incline is 12degrees to the horizontal. What is the combined weight of the boat and its trailer?
Question content area bottom
Part 1
Find the combined weight of the boat and its trailer.
enter your response here lb
(Round to the nearest pound as needed.)
In order to find the combined weight of the boat and its trailer, we need to calculate the component of weight that acts parallel to the incline of the ramp (force required to hold the boat and trailer in place).
First, calculate the force of gravity acting on the boat and trailer:
Force of gravity = mass x acceleration due to gravity
Let's represent the combined weight of the boat and trailer as W.
Component of weight parallel to the incline = Wsin(12°)
Now, we know that this weight must be equal to the force required to hold the boat and trailer in place, which is 600 pounds.
Therefore, Wsin(12°) = 600
W = 600 / sin(12°)
Calculating this, we get:
W ≈ 1977 pounds
So, the combined weight of the boat and its trailer is approximately 1977 pounds.