Answer:
0.5099646386 radians
Explanation:
Δy = 7.5 m
Δx = 10 m
g = 9.8 m sec⁻²
From trigonometry,
Vy₀ = v₀ sin θ
Vy₀² = v₀² sin²θ
From the equations of constant acceleration kinematics,
Vy₀² = 2g Δy
Two things that are equal to the same thing are equal to each other, so
v₀² sin²θ = 2g Δy
v₀² sin²θ = 147 m² sec⁻²
The double angle formula for the sine,
sin²θ = 0.5 [1 − cos(2θ)]
0.5 v₀² [1 − cos(2θ)] = 147 m² sec⁻²
v₀² = 294 m² sec⁻² / [1 − cos(2θ)]
The range equation,
Δx = v₀² sin(2θ) / (2g)
10 m = 294 m² sec⁻² sin(2θ) / {(2g) [1 − cos(2θ)]}
1.5 sin(2θ) = 1 − cos(2θ)
1.5 sin(2θ) = 1 − √[1−sin²(2θ)]
A convenient substitution.
u = sin(2θ)
2.25 u² = 1 − 2√[1−u²] + 1 − u²
3.25 u² − 2 = −2√[1−u²]
1 − 1.625u² = √[1−u²]
1 − 3.25u² + 2.640625u⁴ = 1−u²
2.640625u⁴ − 2.25u² = 0
As long as u≠0,
2.640625u² − 2.25 = 0
2.640625u² = 2.25
u = 0.8520710059
θ = 0.5 arcsin u
θ = 0.5099646386 radians
Furthermore,
v₀ = 15.16666667 m/s
Answer: The first one
Explanation: I think it's the first one because it says what is the "least" gravitational potential energy story between the prairie dog and Earth that said resting in its borrow is using less energy
The fish is dependent on its gill
i am not sure