Answer:
θ ≈ 65°
Explanation:
From the question given above, the following data were obtained:
Maximum height (H) = 8 m
Range (R) = 15 m
Initial velocity (u) = v
Angle θ =?
H = u²Sine²θ / 2g
8 = v²Sine²θ / 2g
Cross multiply
8 × 2g = v²Sine²θ
16g = v²Sine²θ
Divide both side by Sine²θ
v² = 16g / Sine²θ.... (1)
R = u²Sine2θ / g
15 = v²Sine2θ / g
Cross multiply
15 × g = v²Sine2θ
15g = v²Sine2θ
Divide both side by Sine2θ
v² = 15g / Sine 2θ... (2)
Summary:
v² = 16g / Sine²θ.... (1)
v² = 15g / Sine 2θ... (2)
Equate equation 1 and 2
16g / Sine²θ = 15g / Sine 2θ
16 / Sine²θ = 15 / Sine 2θ
Recall:
Sine²θ = SineθSineθ
Sine 2θ = 2SineθCosθ
16 / Sine²θ = 15 / Sine 2θ
16 / SineθSineθ = 15 / 2SineθCosθ
16 / Sineθ = 15 / 2Cosθ
Cross multiply
15 × Sineθ = 16 × 2Cosθ
15Sineθ = 32Cosθ
Divide both side by Cosθ
15Sineθ / Cosθ = 32
Divide both side by 15
Sineθ / Cosθ = 32/15
Recall:
Sineθ / Cosθ = Tanθ
Sineθ / Cosθ = 32/15
Tanθ = 32/15
Tanθ = 2.1333
Take the inverse of Tan
θ = Tan¯¹ 2.1333
θ ≈ 65°
Solution
Explanation:
A solution is a mixture that has the same composition, color, density and taste throughout. They are homogeneous mixtures of solutes and solvents.
- In a solution the solutes are uniformly distributed in the solvent.
- Solutes the particles or substances that are dissolved in the liquid or medium called the solvent.
- Particles of a solution will pass through permeable membranes.
- They do not settle on standing.
Learn more:
Heterogeneous mixtures brainly.com/question/1446244
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The angle of the planet is mathematically given as
dY= 704 degrees
<h3>What angle has planet Y rotated through during this time?</h3>
With Kepler's third rule, which states that a planet's orbit squared is a function of cubed radius, we can prove that this is the case.
Generally, the equation for the period is mathematically given as
(periodX / periodY)^2 = (radius X / radius Y)^3
Therefore
(pX / pY)^2 = 4^3
(pX / pY)^2 = 64
\sqrt{(pX / pY )^2}= \sqrt{64}
(pX / pY=8
In conclusion, Because it takes 8 times longer to complete one orbit on planet X, planet Y travels 8 times farther than planet X does in the same time period...
planet Y travels ;
dY=8 * 88.0
dY= 704 degrees
Read more about Kepler's third rule
brainly.com/question/1086445
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Before a star is born, the matter that will become the star exists as a interstelar gas and dust. The stars are formed as a result of the forces:the force of gravity compresses atoms in the interstellar gas. Then the fusion reaction begins. During this fusion reaction the temperature gets extremely high and all the material evolves into a hot bright star.