David is pushing the handle of a push broom with a force of 190 N at an angle of 33° with the ground. Resolve the force into its horizontal and vertical components and find their magnitudes.(Round your answers to the nearest whole number)
Question
David is pushing the handle of a push broom with a force of 190 N at an angle of 33° with the ground. Resolve the force into its horizontal and vertical components and find their magnitudes.(Round your answers to the nearest whole number)
Solution
To resolve the force into its horizontal and vertical components, we can use the following formulas:
Horizontal component (Fh) = F * cos(θ) Vertical component (Fv) = F * sin(θ)
where F is the magnitude of the force and θ is the angle with the ground.
Given that F = 190 N and θ = 33°, we can substitute these values into the formulas:
Fh = 190 N * cos(33°) Fv = 190 N * sin(33°)
Using a calculator, we find:
Fh = 190 N * cos(33°) = 159 N Fv = 190 N * sin(33°) = 104 N
So, the horizontal component of the force is approximately 159 N and the vertical component is approximately 104 N.
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