This wave, in total, is 30m. What is it's wavelength? * Your answer
2 answers:
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Answer:
K_{total} = 19.4 J
Explanation:
The total kinetic energy that is formed by the linear part and the rotational part is requested
let's look for each energy
linear
= ½ m v²
rotation
= ½ I w²
the moment of inertia of a solid sphere is
I = 2/5 m r²
we substitute
= ½ mv² + ½ I w²
angular and linear velocity are related
v = w r
we substitute
K_{total} = ½ m w² r² + ½ (2/5 m r²) w²
K_{total} = m w² r² (½ + 1/5)
K_{total} = m w² r²
let's calculate
K_{total} = 6.40 16.0² 0.130²
K_{total} = 19.4 J
Apply the Pythagorean theorem to get the resultant velocity:
V =
Given values:
Vx = 57.8m/s
Vy = 5.6m/s
Plug in and solve for V:
V = 58.1m/s
EDIT: Let's get the direction of the resultant velocity as well.
This equation will give the angle of the velocity as measured off of the ground:
θ = tan⁻¹(Vy/Vx)
Again, the given values are:
Vx = 57.8m/s
Vy = 5.6m/s
Plug in the values and solve for the angle θ:
θ = tan⁻¹(5.6/57.8)
θ = 5.5°
The resultant velocity is oriented 5.5° off the ground.