A. The angle at which the arrow must be released to hit the bull's-eye is 20.7 °
B. The arrow will go over the branch.
<h3>A. How to determine the angle</h3>
- Range (R) = 74 m
- Initial velocity (u) = 33 m/s
- Acceleration due to gravity (g) = 9.8 m/s²
- Angle (θ) = ?
R = u²Sine(2θ) / g
74 = 33² × Sine (2θ) / 9.8
Cross multiply
74 × 9.8 = 33² × Sine (2θ)
725.2 = 1098 × Sine (2θ)
Divide both sides by 1098
Sine (2θ) = 725.2 / 1098
Sine (2θ) = 0.6605
Take the inverse of sine
2θ = Sine⁻¹ 0.6605
2θ = 41.3
Divide both sides by 2
θ = 41.3 / 2
θ = 20.7 °
<h3>B. How to determine if the arrow will go over or under the branch</h3>
To determine if the arrow will go over or under the branch situated mid way, we shall determine the maximum height attained by the arrow. This can be obtained as follow:
- Initial velocity (u) = 33 m/s
- Acceleration due to gravity (g) = 9.8 m/s²
- Angle (θ) = 20.7 °
- Maximum height (H) = ?
H = u²Sine²θ / 2g
H = [33² × (Sine 20.7)²] / (2 ×9.8)
H = 6.94 m
Thus, the maximum height attained by the arrow is 6.94 m which is greater than the height of the branch (i.e 3.50 m).
Therefore, we can conclude that the arrow will go over the branch
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The law of reflection states that the angle of reflection is equal to the angle of Incidence .
Answer:
B. Millions of years of high pressure and temperature.
- Millions of years of high pressure and temperature the ancient forests turn into fossil fuels.
Explanation:
Fossil fuels were formed from the dead remains of living organisms millions of years ago. They were formed under high pressure and high temperature.
- Coal : about 300 million years ago the earth had this forest in low lying wetland areas. Due to natural processes like flooding, these forest god buried under the soil. As more soil deposited over them, they were compressed. Under high pressure and high temperature, dead plants got slowly converted into coal.
- Petroleum : Petroleum was formed from organisms living in the sea. As these organisms died, their bodies settled at the bottom of the sea and got covered with layers of soil and clay. Over millions of years, absence of air, high pressure and high temperature transformed the dead organisms into Petroleum.
Coal, Petroleum and natural gas are fossil fuels.
Answer:
a. 
b.
Explanation:
#Apply surface charge density, electric field, and Gauss law to solve:
a. Surface charge density is defined as charge per area denoted as 
, and the strength of the electric field outside the sphere 
Using Gauss Law, total electric flux out of a closed surface is equal to the total charge enclosed divided by the permittivity.
#surface charge outside sphere.
Hence, the new charge density on the outside of the sphere is
b. The strength of the electric field just outside the sphere is calculated as:
From a above, we know the new surface charge to be ,
Hence, the strength of the electric field just outside the sphere is
Answer:
Part a)
When spring compressed by 2 cm
H = 1.47 m
Part b)
When spring is compressed by 4 cm
H = 5.94 m
Explanation:
Part a)
As we know that the spring is compressed and released
so here spring potential energy is converted into gravitational potential energy at its maximum height
So we will have
so we have
Part b)
Similarly when spring is compressed by 4 cm
then we have
so we have
