Answer :
The angle of the incline is approximately 16.65 degrees.
To find the angle of the incline, we can use the kinematic equations and the principles of motion along an inclined plane.
Given:
Mass of the crate (m) = 37.6 kg
Length of the incline (s) = 4.77 m
Time taken to reach the bottom (t) = 1.69 s
Acceleration due to gravity (g) = 9.8 m/s²
Let's consider the motion of the crate along the incline.
Using the equation for displacement along an inclined plane:
s = (1/2) * g * t²
We can rearrange this equation to solve for g:
g = (2 * s) / t²
Substituting the given values:
g = (2 * 4.77 m) / (1.69 s)²
g ≈ 2.8 m/s²
The acceleration due to gravity (g) acting parallel to the incline is given by:
g_parallel = g * sin(θ)
where θ is the angle of the incline.
Rearranging the equation, we can solve for sin(θ):
sin(θ) = g_parallel / g
sin(θ) = g_parallel / 9.8 m/s²
Substituting the value of g_parallel:
sin(θ) = 2.8 m/s² / 9.8 m/s²
sin(θ) ≈ 0.2857
To find the angle θ, we can take the inverse sine (sin⁻¹) of both sides:
θ = sin⁻¹(0.2857)
θ ≈ 16.65°
Therefore, the angle of the incline is approximately 16.65 degrees.
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