Based on the information provided, we can infer and logically deduce the following salient points and parameters:
This ultimately implies that, the horizontal distance covered by this water slide represents the opposite side of a right-angled triangle and as such we would apply Pythagorean theorem.
Mathematically, Pythagorean theorem is given by this formula:
c² = a² + b²
Where:
Substituting the given parameters into the formula, we have;
20.0² = 15.0² + b²
b² = 20.0² - 15.0²
b² = 400.0 - 225.0
b² = 175.0
b = √175.0
b = 13.23 meters.
Thus, we would apply sine trigonometry to determine the magnitude of the first complimentary angle (θ₁) formed by this right-angled triangle:
Sinθ₁ = Opp/Hyp
Sinθ₁ = 13.23/20.0
Sinθ₁ = 0.6615
θ₁ = sin⁻¹(0.6615)
θ₁ = 41.41°.
We know that θ is the angle formed between the water slide and the horizontal plane. Thus, we would determine the magnitude of this second complimentary angle (θ₂):
θ = θ₁ + θ₂
90° = 41.41° + θ₂
θ₂ = 90° - 41.41°
θ₂ = 48.59°.
From the above, we have:
Sinθ₂ = Sin(48.59) = 0.75.
Cosθ₂ = Cos(48.59) = 0.66.
Tanθ₂ = Tan(48.59) = 1.134.
Mathematically, the weight of a physical body (object) can be calculated by using this formula:
Weight = mg
Weight = mass × acceleration due to gravity
Weight = 40.0 × 9.8
Weight = 392 Newton.
Mathematically, the magnitude of the normal force Eric receives from the water slide is given by:
Normal force = mgcosθ
Normal force = 40.0 × 9.8 × cos(48.59)
Normal force = 392 × 0.66
Normal force = 258.72 Newton.
Mathematically, the magnitude of the normal force Eric gives the water slide is given by:
Normal force, Fₙ = mgcosθ
Normal force, Fₙ = 40.0 × 9.8 × cos(48.59)
Normal force, Fₙ = 392 × 0.66
Normal force, Fₙ = 258.72 Newton.
Mathematically, the magnitude of his gravitational force's component parallel to the water slide is given by:
F = Wsinθ = mgsinθ
F = 40.0 × 9.8 × sin(48.59)
F = 392 × 0.75
F = 294 Newton.
Mathematically, the magnitude of the friction force between Eric and the water slide is given by:
Fs = μ_s(Fₙ)
Fs = 0.10 x 258.72 N
Fs = 25.872 Newton.
First of all, we would determine the net force acting on Eric?
F(net) = F - Fs
F(net) = 294 - 25.872
F(net) = 268.13 Newton.
From Newton's second law of motion, acceleration is given by this formula:
Acceleration = Net force/Mass
Acceleration = 268.13/40.0
Acceleration = 6.70 m/s².
In this scenario, we would calculate Eric's speed by using the third equation of motion:
V² = U² + 2aS
V² = 0² + 2(6.70)(20.0)
V² = 268
V = √268
V = 16.37 m/s.
At least, the superman has to apply the following force to prevent Emily from sliding:
Force = Weight - Normal force
Force = 392 - 258.72
Force = 133.28 Newton.
Learn more about frictional force here: https://brainly.com/question/28151607
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